12.5 Probability Of Independent Events Algebra 2

Probabilities of Independent Events Independent: the occurrence of one has no effect on the other occurrence of the other. Example: Tossing a coin twice, the outcome of the first toss (heads or tails) has no effect on the outcome of the second toss Probability of Independent Events If A and B are independent events, then the probability that both A and B occur is P(A and B) = P(A) • P(B)

Example: A game machine claims that 1 in every 15 people win. What is the probability that you will win twice in a row? In a survey 9 out of 11 men and 4 out of 7 women said they were satisfied with a product. If he next 3 customers are 2 women and a man, what is the probability that they will all be satisfied?

Examples: A bag contains 3 red marbles, 7 white marbles, and 5 blue marbles. You draw 3 marbles, replacing each one before drawing the next. What is the probability of drawing a red, then a blue, and then a white marble?

Examples: In a survey 9 out of 11 men and 4 out of 7 women said they were satisfied with a product. If 4 men are the next customers, what is the probability that at least one of them is not satisfied. An auto repair company finds that 1 in 100 cars has had to return for the same problem. How many times can you bring your car to this company before the probability that you have to have your car repaired for the same problem at last once reaches 75%?

Example: 1 in 10,000 cars has a defect. How many of these cars can a car dealer sell before the probability of selling at least one with a defect is 20%?

Probabilities Of Dependent Events Dependent events: the occurrence of one affects the occurrence of the other. Conditional Probability: the probability that an event will occur given that another event has occurred. (B given A is written as P(B A) Probability of Dependent Events If A and B are dependent events, then the probability that both A and B occur is P(A and B) = P(A) • P(B A)

Examples: The table shows the camp attendance for three age groups of students in one town. Find (a) the probability that a listed student attended camp and (b) the probability that a child in the 8 – 10 age group from the town did not attend camp. What is the probability that a listed student was in the 11 – 13 bracket? Age Attended Camp No Camp 5 – 7 45 117 8 – 10 94 62 11 – 13 81 79

Examples: You randomly selected two cards from a standard 52-card deck. Find the probability that the first card is a diamond and the second card is red if (a) you replace the first card before selecting the second, (b) you do not replace the first card. You randomly selected two cards from a standard 52-card deck. What is the probability that the first card is a face card and the second one is not a face card if (a) you replace the first card before selecting the second card, and (b) you do not replace the first card?

Example: Three children have a choice of 12 summer camps that they can attend. If they each randomly choose which camp to attend, what is the probability that they attended all different camps? A family of 4 is each choosing 1 of 8 possible vacations. What is the probability that each family member picks a different vacation?

Example: In one town 95% of the students graduate from high school. Suppose a study showed that at age 25, 81% of the high school graduates held full- time jobs, while only 63% of those who did not graduate held full-time jobs. What is the probability that a randomly selected student from the town will have a full-time job at age 25?

Example: Suppose a survey of high school students shoed that 47% of them worked during the summer. Of those who worked, 62% said they watched 2 hours or more of television per day during the summer. Of those who did not work, 79% watched 2 hours or more. What is the probability that a randomly chosen high school student watched fewer that 2 hours of television during the summer?