8.8 Computation of Compound Probabilities

8.8 Computation of Compound Probabilities 8-1 

8.8 Computation of Compound Probabilities 

P(A � B) 

Objectives 

1. Compute Probabilities of Compound Events 

2. Compute Probabilities of Independent Events 

In the previous section, we discussed how to compute the probability of a single 

event. For example, the probability of being dealt the very rare poker hand, 

1 

called a royal flush, is C(52,5) , about one in two and one-half 

million. 

In this section, we will discuss how to find the probability of one event or 

another, or the probability of one event and another. Such events are called 

compound events. 

� 

C(5, 5) 

1 

C(52, 5) 2,598,960 

� 

1. Compute Probabilities of Compound Events 

We have seen that if and are two events, the probability that and will both 

occur is . In this section, we also discuss , the probability that 

either or will occur. 

Suppose we want to find the probability of drawing a king or a heart from a 

standard card deck. If is the event “drawing a king” and is the event “drawing 

a heart,” then , and P(H) � . However, the probability of drawing a 

king or a heart is not the sum of these two probabilities. Because the king of 

hearts was counted twice, once as a king and once as a heart, and because the 

1 

1 

probability of drawing the king of hearts is 52, 

we must subtract 52 from the sum 

4 13 

of and to get the correct probability. 

13 

P(K) � 52 

4 

A B 

A B 

P(A � B) 

P(A � B) 

A B 

K 

H 

52 

52 

52 

� 4 

� 

13 

16 

� 

52 

4 

P(king or heart) � P(king) � P(heart) � P(king of hearts) 

P(K � H) � P(K) � P(H) � P(K � H) 

13 1 

� � 

52 52 52 

In general, we have the following rule. 

If A and B are two events, then 

P(A � B) � P(A) � P(B) � P(A � B) 

If events A and B have no outcomes in common, then A � B �� and 

P(A � B) � P(�) � 0. 

Such events are called mutually exclusive (if one event 

occurs, the other cannot). 

Here some examples of events that are mutually exclusive and some that are 

not.

8-2 Chapter 8 Natural-Number Functions and Probability 

P(A � B) 

Comment 

A 

is also known as the complement 

of event A. 

P(A) 

Mutually exclusive events Non-mutually exclusive events 

Giving birth to a boy or a girl Giving birth to a boy or a baby 

weighing more than 6 pounds 

Rolling a 2 or 3 on one roll of a die Rolling a 2 or an even number on one 

roll of a die 

Drawing an ace or a king on one draw Drawing an ace or a red card from a 

from a standard card deck standard card deck 

The following rule applies to mutually exclusive events. 

If A and B cannot occur simultaneously, then 

P(A � B) � P(A) � P(B) 

The event A (read as “not A”) 

contains all outcomes of the sample space that 

are not elements of event A. 

Because the events A and A are mutually exclusive, 

P(A � A) � P(A) � P(A) 

Because either event A or event A must happen, P(A � A) � 1. 

Thus, 

P(A � A) � 1 

P(A) � P(A) � 1 

P(A) � 1 � P(A) 

Add �P(A) to both sides. 

This result gives another property of compound probabilities. 

If A is any event, then 

P(A) � 1 � P(A) 

EXAMPLE 1 A counselor tells a student that his probability of earning a grade of D in algebra 

1 

1 

is 5 and his probability of earning an F is 25. 

Find the probability that the student 

earns a C or better. 

Solution Because “earning a D” 

and “earning an F” 

are mutually exclusive, the probability 

of earning a D or F is given by 

� 6 

� 

25 

1 

P(D � F) � P(D) � P(F) 

1 

� 

5 25 

Note that P(D and F) � 0. 

The probability that the student will receive a C or better is 

� 19 

� 1 � 

25 

6 

P(C or better) � 1 � P(D � F) 

25

The probability of earning a C or better is . 

Self Check 1 Find the probability that the student passes (earns a D or better). 

Independent Events 

Formula for P(A � B) 

2. Compute Probabilities of Independent Events 

If two events do not influence each other, they are called independent events. 

The events A and B are said to be independent events if and only if 

P(B) � P(B ƒ A) . 

Here are some examples of events that are independent and some that are not. 

Independent events Non-independent events 

Drawing an ace and a king on two Drawing an ace and a king on two 

draws from a standard card deck draws from a standard card deck 

with replacement without replacement 

A basketball player making ten free A women catching a cold and 

throws in a row developing a cough 

A student scoring two A’s on two tests The chance it will rain and the chance 

the sidewalks get wet 

In the previous section, we discussed the multiplication property for probabilities: 

P(A � B) � P(A) � P(B ƒ A) 

Substituting P(B) for P(B ƒ A) in this property gives a formula for computing 

probabilities of compound independent events. 

If A and B are independent events, then 

P(A � B) � P(A) � P(B) 

The event A of “drawing an ace from a standard deck of cards” and the event 

B of “tossing heads” on one toss of a coin are independent events, because neither 

event influences the other. Consequently, 

� 1 

� 

26 

4 

P(A � B) � P(A) � P(B) 

P(drawing an ace and tossing heads) � P(drawing an ace) � P(tossing heads) 

1 

� 

52 2 

EXAMPLE 2 The probability that a baseball player can get a hit is 3. 

Find the probability that 

she will get three hits in a row. 

Solution Assume that the three times at bat are independent events: One time at bat does 

not influence her chances of getting a hit on another turn at bat. Because 

, , and P(E3) � , 

1 

P(E2) � 1 

P(E1) � 1 

3 

3 


3 

19 

25 

1


P(E1 � E2 � E3) � 1 1 1 1 

� � � 

3 3 3 27 

The probability that she will get three hits in a row is . 

Self Check 2 The probability that another player can get a hit is 4. 

Find the probability that she 

will get four hits in a row. 

EXAMPLE 3 A die is rolled three times. Find the probability that the outcome is 6 on the first 

roll, an even number on the second roll, and an odd prime number on the third roll. 

Solution The probability of a 6 on any roll is . Because there are three even integers 

represented on a die, the probability of rolling an even number is 

. 

Since 3 and 5 are the only odd prime numbers on a die, the probability of 

rolling an odd prime is P(odd prime) � P(O) � . 

Because these three events are independent, the probability of the events happening 

in succession is the product of the probabilities: 

2 

P(even number) � P(E) � 

1 

6 � 3 

3 

P(6) � 

1 

6 � 2 

1 

6 

� 1 

� 

36 

1 

P(six and even number and odd prime) � P(6 � E � O) 

� P(6) � P(E) � P(O) 

1 1 

� � 

6 2 3 

Self Check 3 Find the probability that the outcome is five on the first roll, an odd number on 

the second roll, and two on the third roll. 

EXAMPLE 4 The probability that a drug will cure dandruff is 8. 

However, if the drug is used, 

1 

the probability that it will cause side effects is 6. 

Find the probability that a patient 

who uses the drug will be cured and will suffer no side effects. 

Solution The probability that the drug will cure dandruff is . The probability of 

having side effects is P(E) � . The probability that the patient will have no side 

effects is 

1 

P(C) � 

6 

1 

8 

P(E) � 1 � P(E) � 1 � 1 5 

� 

6 6 

Since these events are independent, 

� 5 

� 

48 

1 

P(cure and no side effects) � P(C � E) 

� P(C) � P(E) 

5 

� 

8 6 

1 

1 

1 

27


Self Check 4 Find the probability that the patient will be cured and suffer side effects. 

24 

25 

1 

256 

1 

72 

Self Check Answers 1. 2. 3. 4. 1 

8.8 Exercises 

Vocabulary and Concepts Fill in the blanks. 

1. A event is one event or another or one 

2. 

event followed by another. 

P(A � B) � 

3. If A and B are 

P(A � B) � P(A) � P(B) . 

, then 

4. The event A is read as “ .” 

5. P(A) � 

6. Two events, A and B, 

are called independent events 

when . 

7. If A and B are independent events, then 

P(A � B) � . 

8. If two events do not influence each other, they are 

called events. 

Practice Assume that you draw one card from a standard 

card deck. Find the probability of each event. 

9. Drawing a black card 

10. Drawing a jack 

11. Drawing a black card or an ace 

12. Drawing a red card or a face card 

Assume that you draw two cards from a standard card 

deck, without replacement. Find the probability of each 

event. 

13. Drawing two aces 

14. Drawing three aces 

15. Drawing a club and then another black card 

16. Drawing a heart and then a spade 

Assume that you roll two dice once. Find the 

probability of each result. 

17. Rolling a sum of 7 or 6 

18. Rolling a sum of 5 or an even sum 

19. Rolling a sum of 10 or an odd sum 

20. Rolling a sum of 12 or 1 

48 

Assume that you have a bucket containing 7 beige 

capsules, 3 blue capsules, and 6 green capsules. You 

make a single draw from the bucket, taking one 

capsule. Find the probability of each result. 

21. Drawing a beige or a blue capsule 

22. Drawing a green capsule 

23. Not drawing a blue capsule 

24. Not drawing either a beige or a blue capsule 

Assume that you are using the same bucket of capsules 

as in Exercises 21–24. 

25. On two draws from the bucket, find the probability 

of drawing a beige capsule followed by a green 

capsule. (Assume that the capsule is returned to 

the bucket after the first draw.) 

26. On two draws from the bucket, find the probability 

of drawing one blue capsule and one green 

capsule. (Assume that the capsule is not returned 

to the bucket after the first draw.) 

27. On three successive draws from the bucket 

(without replacement), find the probability of 

failing to draw a beige capsule. 

28. Jeff rolls a die and draws one card from a card 

deck. Find the probability of his rolling a 4 and 

drawing a four. 

29. Birthday problem Three people are in an elevator 

together. Find the probability that all three 

were born on the same day of the week. 

30. Birthday problem Three people are on a bus 

together. Find the probability that at least one 

was born on a different day of the week from the 

others. 

31. Birthday problem Five people are in a room 

together. Find the probability that all five were 

born on a different day of the year. 

32. Birthday problem Five people are on a bus 

together. Find the probability that at least two of 

them were born on the same day of the year.


33. Sharing homework If the probability that Rick 

1 

will solve a problem is 4 and the probability that 

2 

Dinah will solve it is 5, 

find the probability that at 

least one of them will solve it. 

34. Signaling A bugle is used for communication at 

camp. The call for dinner is based on four pitches 

and is five notes long. If a child can play these 

four pitches on a bugle, find the probability that 

the first five notes that the child plays will call the 

camp to dinner. (Assume that the child is equally 

likely to play any of the four pitches each time a 

note is blown.) 

A woman visits her cabin in Canada. The probability 

1 

that her lawnmower will start is 2, 

the probability that 

1 

her gas-powered saw will start is 3, 

and the probability 

3 

that her outboard motor will start is 4. 

Find each 

probability. 

35. That all three will start 

36. That none will start 

37. That exactly one will start 

38. That exactly two will start 

Applications 

39. Immigration Three children leave Thailand to 

start a new life in either the United States or 

France. The probability that May Xao will go to 

1 

1 

France is 3, 

that Tou Lia will go to France is 2, 

1 

and that May Moua will go to France is 6. 

Find 

the probability that exactly two of them will end 

up in the United States. 

40. Preparing for the GED The administrators of a 

program to prepare people for the high school 

equivalency exam have found that 80% of the students 

require tutoring in math, 60% need help in 

English, and 45% need work in both math and 

English. Find the probability that a student 

selected at random needs help with either math or 

English. 

41. Insurance losses The insurance underwriters 

have determined that in any one year, the probability 

that George will have a car accident is 0.05, 

and that if he has an accident, the probability 

that he will be hospitalized is 0.40. Find the probability 

that George will have an accident but not 

be hospitalized. 

42. Grading homework One instructor grades homework 

by randomly choosing 3 out of the 15 problems 

assigned. Bill did only 8 problems. What is 

the probability that he won’t get caught? 

Discovery and Writing 

43. Explain the difference between dependent and 

independent events, and give examples of each. 

44. Explain why a. P(A ƒ A) � 1 

and 

b. P(A ƒ A) � 0. 

Review Maximize P subject to the given constraints. 

45. P � 2x � y 

46. P � 3x � y 

x � 0 

y � 0 

μ 

x � 4 

x � 2y � 8 

μ 

x � 0 

y � 0 

y � 2 

x � 2 

x � y � 3

8.9 Odds and Mathematical Expectation 

Odds 

Comment 

Note that the odds for an event is 

the reciprocal of the odds against 

the event. 

Objectives 

1. Define and Compute Odds 

2. Define and Compute Mathematical Expectation 

8.9 Odds and Mathematical Expectation 8-7 

At the horse races, you will often hear phrases such as 

Sweet Pea is a long shot with odds of 30 to 1. 

or 

The odds on Barbaro are 8 to 5. 

Since the concept of odds is closely related to the concept of probability, the 

payoffs on bets at the track are based on the odds for each horse in a race. 

When we say that the odds on Sweet Pea are 30 to 1, we generally mean that 

the odds against the horse are 30 to 1. As we will soon see, this is equivalent to 

1 1 

saying that the probability of Sweet Pea winning is 30 � 1 � 31. 

When we say that 

the odds on Barbaro are 8 to 5, we mean that the probability of Barbaro winning 

5 5 

is 8 � 5 � 13. 

We will begin this section by discussing odds. 

1. Define and Compute Odds 

The odds for an event is the probability of a favorable outcome divided by the 

probability of an unfavorable outcome. 

The odds against an event is the probability of an unfavorable outcome divided 

by the probability of a favorable outcome. 

EXAMPLE 1 The probability that a horse will win a race is 4. 

Find the odds for and the odds 

against the horse. 

Solution Because the probability that the horse will win is 4, 

the probability that the horse 

3 

will not win is . The odds for the horse are 

probability of a win 

probability of a loss � 

or 1 to 3. The odds against the horse are 

probability of a loss 

probability of a win � 

or 3 to 1. 

4 

1 

4 

3 

4 

3 

4 

1 

4 

� 1 

3 

� 3 

� 3 

1 

1 

1


Self Check 1 The probability that a horse will lose a race is 5. 

Find the odds for and the odds 

against the horse. 

Another way to find the odds in favor of an event is to divide the number of 

1 

favorable outcomes by the number of unfavorable outcomes. In Example 1, this is 3. 

To find the odds against an event, divide the number of unfavorable outcomes 

3 

by the number of favorable outcomes. In Example 1, this is . 

EXAMPLE 2 The odds against a horse are 30 to 1. Find: a. the probability that the horse will 

lose b. the probability that the horse will win 

Solution If p is the probability that the horse will lose, then 1 � p is the the probability that 

the horse will win. By definition, we have 

p � 30 

p � 30 � 30p 

31p � 30 

31 

30 

probability of losing 

Odds against an event � 

probability of winning 

p 

� 

1 1 � p 

Multiply both sides by 1 � p. 

Add 30p to both sides. 

Divide both sides by 31. 

The probability that the horse will lose is . The probability that the horse will 

win is 1 � . 

30 

31 

1 

� 

Self Check 2 The odds against a horse are 8 to 5. Find the probability that the horse will win. 

2. Define and Compute Mathematical Expectation 

Suppose we have a chance to play a simple game with the following rules: 

1. Roll a single die once. 

2. If a 6 appears, win $3. 

3. If a 5 appears, win $1. 

4. If any other number appears, win 50¢ . 

5. The cost to play (one roll of the die) is $1. 

In this game, the probability of any one of the six outcomes—rolling a 6, 5 4, 

1 

3, 2, or 1—is 6, 

and the winnings are $3, $1, and 50¢ . The expected winnings E can 

be found by using the following equation and simplifying the right side: 

E � 1 

6 

31 

31 

(3) � 1 

6 

(1) � 1 

6 

(0.50) � 1 

6 

� 

� 1 

1 

6 (6) 

� 1 

(3 � 1 � 0.50 � 0.50 � 0.50 � 0.50) 

6 

30 

1 

1 1 

(0.50) � (0.50) � 

6 6 (0.50) 

1

Mathematical 

Expectation 

Over the long run, we could expect to win $1 with every play of the game. 

Since it costs $1 to play the game, the expected gain or loss is 0. Because the 

expected winnings are equal to the admission price, the game is fair. 

If a certain event has n different outcomes with probabilities P1, P2, P3, . .., 

Pn and the winnings assigned to each outcome are x1, x2, x3, . . . xn, the 

expected winnings, or mathematical expectation, E is given by 

E � P 1x 1 � P 2x 2 � P 3x 3 � p � P nx n 

EXAMPLE 3 It costs $1 to play the following game: Roll two dice; collect $5 if we roll a sum of 

7, and collect $2 if we roll a sum of 11. All other numbers pay nothing. Is it wise 

to play the game? 

Solution The probability of rolling a 7 on a single roll of two dice is 36, 

the probability of 

2 

28 

rolling an 11 is 36, 

and the probability of rolling something else is 36. 

The mathematical 

expectation is 

E � 6 2 28 17 

(5) � (2) � (0) � � $0.944 

36 36 36 18 

By playing the game for a long period of time, we can expect to get back 

about 95¢ for every dollar spent. For the fun of playing, the cost is about 5¢ a 

game. If the game is enjoyable, it might be worth the expected loss. However, the 

game is slightly unfair. 

Self Check 3 Is it wise to play the game if you win $4 when you roll a sum of 7 and $6 when you 

roll a sum of 11? 

5 

Self Check Answers 1. 4 to 1; 1 to 4 2. 13 3. Yes, the game is fair. 

8.9 Exercises 

Vocabulary and Concepts Fill in the blanks. 

1. The are the probability of a favorable 

outcome divided by the probability of an 

unfavorable outcome. 

2. The are the probability of an 

unfavorable outcome divided by the probability of 

a favorable outcome. 

3. If the odds for an event are 1 to 4, the probability 

of winning is . 

4. Mathematical expectation E is given by 

E � 

. 

Practice 

1 

5. The probability that a horse will win a race is 5. 

Find the odds for and against the horse. 

8.9 Odds and Mathematical Expectation 8-9 

6. The probability that a horse will win a race is 3. 

Find the odds for and against the horse. 

7. The odds against a horse are 50 to 1. Find the 

probability that the horse will win. 


probability that the horse will lose. 

Assume a single roll of a die. 

9. Find the probability of rolling a 6. 

10. Find the odds in favor of rolling a 6. 

11. Find the odds against rolling a 6. 

12. Find the probability of rolling an even number. 

13. Find the odds in favor of rolling an even number. 

6 

2


14. Find the odds against rolling an even number. 

Assume a single roll of two dice. 

15. Find the probability of rolling a sum of 6. 

16. Find the odds in favor of rolling a sum of 6. 

17. Find the odds against rolling a sum of 6. 

18. Find the probability of rolling an even sum. 

19. Find the odds in favor of rolling an even sum. 

20. Find the odds against rolling an even sum. 

Assume that you are drawing one card from a standard 

card deck. 

21. Find the odds in favor of drawing a queen. 

22. Find the odds against drawing a black card. 

23. Find the odds in favor of drawing a face card. 

24. Find the odds against drawing a diamond. 

25. If the odds in favor of victory are 5 to 2, find the 

probability of victory. 

26. If the odds in favor of victory are 5 to 2, find the 

odds against victory. 

27. If the odds against winning are 90 to 1, find the 

odds in favor of winning. 

28. Find the odds in favor of rolling a 7 on a single 

roll of two dice. 

29. Find the odds against tossing four heads in a row 

with a fair nickel. 

30. Find the odds in favor of a couple having four 

girl babies in succession. 1Assume P(girl) � 1 

2 .2 


probability that the horse will win. 


probability that the horse will lose. 

33. It costs $2 to play the following game: 

a. Draw one card from a card deck. 

b. Collect $5 if an ace is drawn. 

c. Collect $4 if a king is drawn. 

d. Collect nothing for all other cards drawn. 

Is it wise to play this game? Explain. 

34. Lottery tickets One thousand tickets are sold 

for a lottery with two grand prizes of $800. Find 

a fair price for the tickets. 

35. Find the odds against a couple having three baby 

boys in a row. 1Assume P(boy) � 

36. Find the odds in favor of tossing at least three 

heads in five tosses of a fair coin. 

37. Suppose you toss a coin five times and collect $5 

if you toss five heads, $4 if you toss four heads, 

$3 if you toss three heads, and no money for any 

other combination. How much should you pay to 

play the game if the game is to be fair? 

38. If you roll two dice one time and collect $10 for 

double 6’s and $1 for double 1’s, what is a fair 

price for playing the game? 

39. Counting an ace as 1, a face card as 10, and all 

others at their numerical values, find the expected 

value if you draw one card from a card deck. 

1 

2 .2 

40. Find the expected sum of one roll of two dice. 

41. A multiple-choice test of eight questions gives 

five possible answers for each question. Only one 

of the answers for each question is right. Find the 

probability of getting seven right answers by 

simple guessing. 

42. In the situation described in Exercise 41, find the 

odds in favor of getting seven answers right. 

Discovery and Writing 

43. If “the odds are against an event,” what can be 

said about its probability? 

44. To disguise the unlikely chance of winning, a 

contest promoter publishes the odds in favor of 

winning as 0.0000000372 to 1. What are the odds 

against winning? 

Review 

45. Find the equation of the line perpendicular to 

3x � 2y � 9 and passing through the point (1, 1) . 

46. Find the equations of the parabolas with vertex 

at the point (3, �2) and passing through the 

origin. 

47. Find the equation of the circle with center at 

(3, 5) and tangent to the x-axis. 

48. Write the equation 

2x 2 � 4y 2 � 12x � 24y � 46 � 0 

in standard form, and identify the curve.

CHAPTER REVIEW 

8.8 Computation of Compound Probabilities 

Definitions and Concepts Examples 

Chapter Review 8-11 

If A and B are two events, then 

Find the probability of drawing an ace or a heart on 

one draw from a standard card deck. 

P(A � B) � P(A) � P(B) � P(A � B) 

4 1 

The probability of drawing an ace is � . 

52 13 

13 1 

The probability of drawing a heart is � . 

52 4 

The ace of hearts has been counted both as an ace 

and as a heart. To get rid of the duplication, we must 

subtract the probability of getting the ace of hearts 

from the sum of the two probabilities listed above. 

� 4 

� 

13 

16 

� 

52 

1 

P(ace or a heart) � P(ace) � P(heart) � P(ace of hearts) 

1 1 

� � 

13 4 52 

If A and B cannot occur simultaneously, then 

Find the probability of drawing a 2 or a 3 from a 

standard card deck. 

P(A � B) � P(A) � P(B) 

4 1 

The probability of drawing a 2 is � . 

52 13 

4 1 

The probability of drawing a 3 is � . 

52 13 

Since there is no duplication, 

� 2 

� 

13 

1 

P(2 or 3) � P(2) � P(3) 

1 

� 

13 13 

If A is any event, then 

If the probability that a horse will win a race is , the 

P(A) � 1 � P(A) 

probability that the horse will lose the race is 

1 � . 

7 

11 

4 

11 � 11 

7


If A and B are independent events, then 

A basketball player makes 80% of her free throws. 

Find the probability that she will make 2 free throws 

P(A � B) � P(A) � P(B) 

in a row. 

The probability that she makes 1 free throw is 

80% � . 

4 

Exercises 

82. On one draw from a standard card deck, find the 

probability of drawing a two or a spade. 

8.9 Odds and Mathematical Expectation 

5 

So the probability that she will make 2 in a row is 

� 4 

P(1 free throw � another free throw) 

� P(1 free throw) � P(another free throw) 

4 16 

� � 

5 5 25 

83. If the probability that a drug cures a disease is 

0.83, and we give the drug to 800 people with the 

disease, find the expected number of people who 

will not be cured. 

Definitions and Concepts Examples 

The odds for an event is the probability of a favorable The probability that a politician will be elected is esti- 

outcome divided by the probability of an unfavorable mated to be 0.7. Find the odds for and against the 

outcome. 

politician. 

The odds against an event is the probability of an 

unfavorable outcome divided by the probability of a 

Odds for the politician or 7 to 3. 

favorable outcome. 

Odds against the politician � or 3 to 7. 

0.3 

� 

3 

� 

0.7 7 

0.7 7 

� 

0.3 3 

A game is fair if the cost to play equals the expected 

winnings E. 

Suppose it costs $5 to play the following game: 

Roll two dice: Collect $10 if you roll a 12 or a 2. 

Otherwise collect $1. 

Is it wise to play the game? 

Since the probability of rolling a 12 is 36, 

of rolling a 

1 

34 

2 is 36, 

and of rolling something else is 36, 

the 

mathematical expectation is 

E � 1 1 34 

(10) � (10) � (1) � 1.5 

36 36 36 

Since it costs $5 to play and the expected earnings are 

only $1.50, this is a foolish game to play. 

1

Exercises 

84. Find the odds against a horse if the probability 

7 

that the horse will win is 8. 

85. Find the odds in favor of a couple having 4 baby 

girls in a row. 

5 

86. If the probability that Joe will marry is 6 and the 

3 

probability that John will marry is 4, 

find the 

odds against either one becoming a husband. 

87. If the odds against Priscilla’s graduation from 

10 

college are 11, 

find the probability that she will 

graduate. 

Chapter Review 8-13 

88. Find the expected earnings if you collect $1 for 

every heads you get when you toss a fair coin 

4 times. 

89. If the total number of subsets that a set with 

elements can have is 2 , explain why 

n 

n 

anb 

� 

0 

a n 

b � 

1 

a n 

2 b � p � 

a n 

b � 2n 

n

8.8 Computation of Compound Probabilities

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