15. Given: P(A) = 0.45, P(B) = 0.65, and P(A and B) = 0.35. Find (a) Construct the Venn Diagram. (b) P( A or B) (c) P(A or B)(6) P(B|A) 16. Find the probability of selecting the same card from a deck of playing cards twice 16. Find the probability of selecting the same card from a deck of playing cards twice (a) with replacement. (b) without replacement. 17. Find the probability of selecting three different people that are randomly selected have the same birth month. 18. Suppose 35% of adults get enough sleep, 45% get enough exercise1 and 25% do both. Use Venn Diagram to nd the probability of the following events: (3} Construct the Venn Diagram. {b} enough sleep and not enough exercise. (c) not enough sleep and enough exercise. ((1) not enough sleep and not enough exercise. (e) enough sleep given enough exercise. 19. The probability that J 056 shoppiiig for himself will buy a tie is 0.2, the probability that he will buy a shirt is 0.3, and the probability that he will buy a tie given that he buys a shirt is 0.4. Find the probability that he will buy (a) both a shirt and a tie. (11):: shirt, 3 tie1 or both. (c) a shirt, given that he buys a tie. 20. A local re station has 3 re engines operating independently. The probability that a specic engine is available when needed is 0.95. (a) What is the probability that neither is available when needed? (b) What is the probability that at least one re engine is available when needed