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Probability- Foundation 1 CABS 3 Gen 120 1. Suppose there are two checkers, red and clack, in a box. Luanne picks one, looks at it, and puts it back. In this case, does the probability of picking a red checker on the second pick depend upon whether she picked a red or a black checker, the first time? Explain: Draw a tree diagram to represent these relationships and to help explain your answer. 2. Jason and Karl own four pairs of jeans, one blue, white, tan and gray pair. Find the probability that both boys will wear gray jeans today. Find P(J and K), where J and K are independent events. From the diagram, list the sample space to show all the possible combinations. Each boy’s jeans are represented by blue, white, tan and gray. The ordered pairs will be in the form Karl’s choice, Jason’s choice. _________________________________ G _________________________________ T Jason W B B W The probability for independent events can be considered another way: Let P(J) = probability of Jason’s wearing gray jeans today Let P(K) = Probability of Karl’s wearing gray jeans today P(J) = ____________________ P(K) = ___________________ P(J and K) = ______________________ page 406 T Karl G 3. Beth has 2 red socks and 4 white socks in her sock drawer. Find the probability that she will randomly select one red sock and then, without replacing it, randomly select another red sock. Find P(red and red) for dependent events. P(red and red) = ___________________________________ Fred has 2 green, 4 blue and 3 red shirts in a drawer. He chooses a shirt at random and does not want a red shirt. Find the probability that Fred will pick a green or blue shirt. Find P(green or blue), for mutually exclusive events. P(green or blue) = _________________________________ Could the probability be calculated in another way? Explain. _______________________________________________________________________ _______________________________________________________________________ 4. Of the 20 members of the bicycle club, 7 were in Race A, 8 were in Race B and 3 were in both races. Find the probability of selecting st random a club member who was in Race A or Race B. Find P(A or B) for mutually inclusive events. Label the diagram to find how many members were racing. P(A or B) = _____________ Describe how the probability could be described in another way. 5. In the formula for inclusive events A and B, P(A or B) = P(A) + P(B) – P(A and B). Explain what P(A and B) represents in the formula, and why it is subtracted from P(A) + P(B). _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ page 407