MATHPOWER TM 12, WESTERN EDITION Chapter 8 Probability

Probability theory is the branch of mathematics used to predict the likelihood that a certain event will occur. An experiment is an action that has measurable or quantifiable results. The sample space for an experiment is the set of all possible outcomes of the experiment. An outcome is a single element of the sample space. An event is any subset of elements of the sample space. In an experiment with outcomes that are equally likely, the probability that a particular event will occur is calculated as: Probability - Definitions

Listing the Sample Space Use a tree diagram to list the sample space for tossing a coin and rolling a die. CoinDieOutcomes H T H, 1 H, 2 H, 3 H, 4 H, 5 H, 6 T, 1 T, 2 T, 3 T, 4 T, 5 T, The Sample Space

Calculating Probability a) Determine the probability of tossing a tail and rolling a one. b) Determine the probability of tossing a head and rolling a five or a six. a) b) Tossing a coin and rolling a die are independent events - the rolling of the die is not affected by the tossing of the coin and vice versa

Using a Probability Tree In a recent survey, it was found that 18% of Canadians have blonde hair and 22% have blue eyes. Assuming blonde hair and blue eyes are independent events: a)Estimate the probability that a randomly-selected Canadian will have blonde hair and blue eyes. b)What is the probability that at least two out of three randomly-selected Canadians will have blonde hair? Blonde Not Blonde Blue Not Blue Blue Not Blue Blonde, Blue Blonde, Not Blue Not blonde, Blue Not Blonde, Not Blue HairEyesOutcomes (0.18 x 0.22) (0.18 x 0.78) (0.82 x 0.22) (0.82 x 0.78)

8.1.6 a) P(Blonde, Blue) = P(Blonde) x P(Blue) = 0.18 x 0.22 = The probability that a Canadian has blonde hair and blue eyes is Blonde Not Blonde Not Blonde Blonde Not Blonde Blonde Not Blonde Blonde Not Blonde Blonde Not Blonde Blonde Not Blonde B, B, B B, B, not B B, not B, B B, not B, not B not B, B, B not B, B, not B not B, not B, B not B, not B Outcomes1st Person 2nd Person3rd Personb) P(at least two blonde) = P(2 blonde) + P(3 blonde) = P(B, B, B) + P(B, B, not B) + P(B, not B, B) + P(not B, B, B) = (0.18 x 0.18 x 0.18) + (0.18 x 0.18 x 0.82) + (0.18 x 0.82 x 0.18) + (0.82 x 0.18 x 0.18) = Using a Probability Tree [cont’d]

Suggested Questions: Pages 371 and , 9, 10, 14 a-d 8.1.7