6-2 Investigating Probability notes

Mrs. Aitken’s Integrated 1 Math
Unit 6 Ratios, Probability, and Similarity
6-2 Investigating Probability
Warm-up
1. Suppose 19 students in a class of 28 are girls. What is the ratio of the number of girls
to the number of students in the class? 19/28
2. In baseball, Steven gets a hit every third time he is at bat. If he bats 6 times in a game,
how many hits will Steven get? 2
3. In softball, Tessa got three hits out of nine times at bat. Using these statistics, what is
the change the she will get a hit the next time she is at bat? 1 out of 3
Find each sum or difference
5
4. 1− = 1/6 6
5.
1 6
+ = 1
4 8
Today we will:
1. Describe how likely it is that something will happen, probability.
Tomorrow we will:
1. Solve proportions.
Investigating Probability
Key Terms
1. Outcome – a possible result of an experiment.
A three way race for Senator involving a Republican, a Democrat, and an
Independents is an experiment with three possible outcomes: the Republican wins, the
Democrat wins, or the Independent wins.
2. Event – a particular outcome or combination of outcomes of an experiment.
In the election described in (1), the event “the Independent loses” can happen in one
of two ways (outcomes): the Republican wins, or the Democrat wins.
3. Probability – a number from 0 to 1, where 0 indicates impossibility and 1 indicates
certainty, that describes how likely it is that an event will occur.
Weather forecasts are given in probabilities (or chances). A “70% chance of rain”
means that the probability of rain is 0.70.
4. Complementary events – two events, the event “E” and the event “E does not
happen”. The sum of the probabilities of complementary events is 1.
In a lottery, the events “you win” and “you lose” are complementary.

Mrs. Aitken’s Integrated 1 Math
Unit 6 Ratios, Probability, and Similarity
Experimental Probability
Experimental probability – probability that is based on the results of an experiment, an
activity in which data is observed and recorded.
Researchers find that a medicine they are testing improved the condition of 270 out of 300
patients. Using experimental probability, they conclude that the probability the medicine will
help a patient who takes it is 270 0.9 or 90%
300 =
The experimental probability of an event E can be calculated using the formula
number of times event E occurs
PE ( ) =
number of times the experiment is done
The more times the experiment is conducted, the more reliable is the computed value of
P(E).
Example 1
A vending machine dispenses five different types of fruit drinks. The owner of the machine
has kept records on the last 2000 sales from the machine.
Fruit Punch 746
Citrus Punch 524
Apple Juice 98
Orange Juice 282
Cranberry Juice 350
What is the probability that a randomly-chosen purchase from the machine will be a punch?
Solution
Of the five types of juice, two are punches: fruit punch and citrus punch.
number of times a punch was purchased
P (purchasing a punch) =
number of times a purchase was made
746 + 525 1270
= = 0.635
2000 2000
The probability that a punch is bought is 0.635 or 63 ½%

Mrs. Aitken’s Integrated 1 Math
Unit 6 Ratios, Probability, and Similarity
Theoretical Probability
Theoretical probability – probability found without having to do an experiment, based on the
assumption that all outcomes of an experiment are equally likely to occur.
You buy two tickets for a charitable lottery. Eighty-five tickets are sold. Since each ticket is
equally likely to be drawn, you can use theoretical probability to reason that your chances of
winning are 2 0.024 or 2.4%
85 =
When all the possible outcomes of an experiment are equally likely, the following ratio is
used to determine the theoretical probability of an event E.
number of outcomes that are in event E
PE ( ) =
number of possible outcomes
If you know the probability of an event E, then the probability that event E does not happen
is 1 – P(E).
Example 2
The letters of the alphabet are printed on cards (one letter per card) and placed in a box. You
close your eyes and choose one card. What is the probability that the card you chose is
a. The first letter of your name?
b. A vowel?
c. Not a vowel?
Solution
Each card is equally likely to be chosen, so theoretical probability can be used.
a. Of the 26 cards, only one has your initial on it.
P(choosing your first initial) = 1/26
b. There are five vowels (A, E, I, O, U) so the event of “choosing a vowel” can happen
in five ways.
P(choosing a vowel) = 5/26
c. “Choosing a vowel” and not “choosing a vowel” are complementary events.
P(not choosing a vowel) = 1 - P(choosing a vowel)
= 1- 5/6
= 21/26