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5. Cain and Abel are equally good in chess. They play 3 games against each other. What is the probability that: a. Cain wins all 3 games? b. Cain wins the first 2 games only? c. Abel wins only 1 game? d. Abel wins at least 2 games? 6. There are five rare books out of the fifteen books on a library shelf. If three books from the shelf were borrowed by a researcher, what is the probability that: a. that none of the rare books is included? b. at least 3 of the rare books are included? 7. The probabilities that Amy and Tess will arrive at a party on time are 2/3 and 3/4, respectively. Find the probability that: a. both Amy and Tess will not arrive on time. b. only one of them will arrive on time. 8. Given the following table for the discrete random variable X. X P(X) 0.2 10% 0.4 20% 0.6 25% 0.8 20% 1.0 25% a. P(X $ 0.6) = b. P(0.25 0.8) 9. The Math Club moderator selects 3 contestants to compete in the tri-meet out 3 female and 2 male contenders. Let the random variable F represent the number of females in the group of 3 contestants. a. Give the sample space and range space for the random variable C. b. Construct the probability mass function and histogram. c. Compute for the mean, variance and standard deviation of C