Mrs. Nguyen – Honors Algebra II – Chapter 13 Notes ... - Teacher

LESSON 13.3 – PROBABILITYSample spaceDefinition ofprobabilityThe sample space of an event is all the possibleoutcomes of an experiment.number of outcomes in the eventProbability number of outcomes in the sample spaceAn event is one or moreoutcomes from the sample space.Example:Practice Problems: Suppose you select 2 letters at random from the word COMPUTE. Find each probability.1. P(2 vowels) 2. P(2 consonants) 3. P(1 vowel and 1 consonant)Practice Problems: Find each probability4. P(the card is a five) 5. P(the card is a five or a six)6. A five-card poker hand is drawn from astandard deck of cards. What is the probability that allfive cards are black?7. Tom has a collection of 32 CDs- 18 R&B and14 country. As he is leaving for a trip, he randomlychooses 6 CDs to take with him. What is theprobability that he selects 3 R&B and 3 country?8. A seven card hand is drawn from a standarddeck of 52 cars. What is the probability that all 7 cardsare hearts?9. A bag contains 20 tennis balls, of which fiveare defective. If two are selected at random from thebag, what is the probability that both are defective?Mrs. Nguyen – Honors Algebra II – Chapter 13 Notes – Page 4

OR (Union)ProbabilityProblemsIf A and B are events in a sample space S,then the probability of A OR B is:P(A or B) = P(A) + P(B) – P(A and B)Two events that cannot occur at the sametime are called mutually exclusive,therefore P(A and B) = 0.Practice Problems: A die is rolled. Find each probability.10. P(1 or 6) 11. P(even or prime) 12. P(multiple of 2 or amultiple of 3)Practice Problem 13: Ten slips of paper are placed in a container. Each is labeled with a number from 1through 10. Find each probability of picking each of the following from the container:a. P(1 or 10) b. P(3 or odd)Practice Problems: Find each probability.14. Two marbles are simultaneously drawn at random from a bag containing 3 red, 5 blue, and 6 greenmarbles.a. P(at least one red marble) b. P(two marbles of the samecolor)P(two marbles of different colors)15. There are 8 girls and 8 boys on ASB. Three ofthe students are juniors. What is the probability that aperson selected from ASB is not a junior?16. Christina has a stack of playing cardsconsisting of 10 hearts, 8 spades, and 7 clubs. If sheselects a card at random from this stack, what is theprobability that it is a heart or a club?Mrs. Nguyen – Honors Algebra II – Chapter 13 Notes – Page 5

Two events are independent if the outcome of thefirst event does not affect the outcome of the 2 nd event.“AND” (Intersection) Probability Problems:Two events are dependent if the outcome of the firstevent does affect the outcome of the 2 nd event.If two events, A and B, are in the same sample space,then the probability of A and B occurring is:PA ( and B) PA ( ) PB ( )Practice Problems: Two cards are drawn from a standard deck of cards. Find each probability if noreplacement occurs.17. P(jack, jack) 18. P(heart, club) 19. P(two diamonds)20. P(2 of hearts, diamond) 21. P(2 red cards) 22. P(2 black aces)Practice Problems: Find each probability.23. Monica has 7 blue pens, 3black pens, and 2 red pens in herdesk. If she selects three pens atrandom with no replacement, whatis the probability that she will firstselect a blue pen, then a black pen,and then another blue pen?24. A black die and a white dieare rolled. What is the probabilitythat a 3 shows on the black die anda 5 shows on the white die?25. A contestant on a gameshow reaches into a containerwithout looking and picks twopaper bills. There are 2 $100 bills,4 $50 bills, 10 $20 bills, and 20 $10bills. What is the probability thatthe contestant draws 2 $10 bills oneafter the other withoutreplacement?Mrs. Nguyen – Honors Algebra II – Chapter 13 Notes – Page 6

LESSON 13.4 – BINOMIAL PROBABILITYBinomialExperimentBinomialProbabilitiesA binomial experiment is one in which there are two outcomes, which we call “success”and “failure”.An experiment has two possible outcomes, S and F (success & failure) which P(S) = pand P(F) = q = 1 – p. The probability of getting exactly r successes in n independentr n rtrials of the experiment is: P(r successes in n trials) = Cnrpq ( , )Practice Problems: A fair die is rolled 8 times, find each probability.1. Exactly 3 rolls are fives 2. At most two rolls are fives 3. At least 5 rolls are fivesPractice Problem 4: Find each probability. Ten percent of a batch of toothpaste is defective. Five tubes oftoothpaste are selected.a. P(0 defective) b. P(exactly one defective)c. P(at least 3 defective) d. P(less than 3 defective)Mrs. Nguyen – Honors Algebra II – Chapter 13 Notes – Page 7