MATHPOWER TM 12, WESTERN EDITION Chapter 8 Probability 8.2A 8.2A.1

8.2A.2 Independent Versus Dependent Events Two events are independent if the probability that each event will occur is not affected by the occurrence of the other event. Two events are dependent if the outcome of the second event is affected by the occurrence of the first event. Classify the following events as independent or dependent: a) tossing a head and rolling a six b) drawing a face card, and not returning it to the deck, and then drawing another face card c) drawing a face card and returning it to the deck, and then drawing another face card independent dependent independent If the probabilities of two events are P(A) and P(B) respectively, then the probability that both events will occur, P(A and B), is: P(A and B) = P(A) x P(B)

Finding Probability 1.A cookie jar contains 10 chocolate and 8 vanilla cookies. If the first cookie drawn is replaced, find the probability of: a) drawing a vanilla and then a chocolate cookie P(V and C) = P(V) x P(C) 8.2A.3 The probability of drawing a vanilla and a chocolate cookie is b) drawing two chocolate cookies P(C and C) = P(C) x P(C) The probability of drawing two chocolate cookies is

8.2A.4 2.Find the probability of drawing a vanilla and then drawing a chocolate cookie, if the first cookie drawn is eaten. P(V and C) = P(V) x P(C) The probability of drawing a vanilla and a chocolate cookie is An aircraft has three independent computer guidance systems. The probability that each will fail is What is the probability that all three will fail? P(all three fail) = P(A) x P(B) x P(C) = x x = The probability that all three will fail is Finding Probability

Probability The sum of all the probabilities of an event is equal to 1. If P = 1, then the event is a certainty. If P = 0, then the event is impossible. In probability, if Event A occurs, there is also the probability that Event A will not occur. Event A not occurring is the compliment of Event A occurring. The probability of Event A not occurring is written as P(A). (This is read as “Probability of not A”). For Event A: P(A) + P(A) = 1 P(A) = 1 - P(A) 8.2A.5 Example: One card is drawn from a deck of 52 cards. What is the probability of each of these events? a) drawing a red four b) not drawing a red four

8.2A.6 Finding the Probability of the Same Birth Month In a group of seven people, what is the probability that at least two have their birthdays in the same month? Find the probabilities of the seven birthdays being in seven different months. 1st person 2nd person 3rd person 5th person 6th person 7th person 4th person P(birthdays in 7 different months) = P(at least 2 birthdays in the same month) = 1 - (different months) = = 0.889

8.2A.7 P(birthdays in 7 different months) = P(at least 2 birthdays in the same month) = 1 – = Finding the Probability of the Same Birth Month [cont’d] Alternative Method: 12 x 11 x 10 x 9 x 8 x 7 x 6 can be expressed as 12 P x 12 x 12 x 12 x 12 x 12 x 12 can be expressed as P(birthdays in 7 different months) P(at least 2 birthdays in the same month) = = 0.889

8.2A.8 Suggested Questions: Pages 380 and , 14, 16, 17 ab

MATHPOWER TM 12, WESTERN EDITION 8.2B 8.2B.9 Chapter 8 Probability

8.2B.10 Classifying Exclusivity Two events are mutually exclusive if they cannot occur simultaneously. For instance, the events of drawing a diamond and drawing a club from a deck of cards are mutually exclusive because they cannot both occur at the same time. For mutually exclusive events: Events that are not mutually exclusive have some common outcomes. For instance, the events of drawing a diamond and drawing a king from a deck of cards are not mutually exclusive because the king of diamonds could be drawn, thereby having both events occur at the same time. For events that are not mutually exclusive: P(A or B) = P(A) + P(B) P(A or B) = P(A) + P(B) - P(A and B)

8.2B.11 Classifying Exclusivity Classify each event as mutually exclusive or not mutually exclusive. a) choosing an even number and choosing a prime number b) picking a red marble and picking a green marble c) living in Edmonton and living in Alberta d) scoring a goal in hockey and winning the game e) having blue eyes and black hair not mutually exclusive mutually exclusive not mutually exclusive

8.2B.12 Probability and Exclusivity 1. A box contains six green marbles, four white marbles, nine red marbles, and five black marbles. If you pick one marble at a time, find the probability of picking a) a green or a black marble. P(G or B) = P(G) + P(B) b) a white or a red marble. P(W or R) = P(W) + P(R)

8.2B.13 Probability and Exclusivity 2. Determine the probability of choosing a diamond or a face card from a deck of cards. P(D or F) = P(D) + P(F) - P(D and F) The probability of choosing a diamond or a face card is

8.2B.14 Probability and Exclusivity 3. A national survey revealed that 12.0% of people exercise regularly, 4.6% diet regularly, and 3.5% both exercise and diet regularly. What is the probability that a randomly-selected person neither exercises nor diets regularly? Find the probability that a person exercises or diets regularly. P(D or F) = P(D) + P(F) - P(D and F) = = Therefore, the probability that a person neither exercises nor diets regularly is: = = 86.9%

8.2B.15 Probability and Exclusivity [cont’d] A national survey revealed that 12.0% of people exercise regularly, 4.6% diet regularly, and 3.5% both exercise and diet regularly. What is the probability that a randomly-selected person neither exercises nor diets regularly? Alternative method: Use a Venn diagram Exerciser Dieter 3.5%1.1% 8.5% Entire Population Therefore, the probability that a person neither exercises nor diets regularly is: 100% - (8.5% + 3.5% + 1.1%) = 86.9%

8.2B.16 Suggested Questions: Pages 380 and , 15, 18, 20