On a surprise quiz consisting of five true-false questions,…

On a surprise quiz consisting of five true-false questions, an unprepared student guesses each answer.Find the probability that he gets at least one correct.(Hint: it’s easier to think about the chances that he doesn’t get at least one correct, i.e. the chances that they’re all wrong. He’s got a 50% chance on each question, and there are 5 independent questions. If we can compute the probability that they’re all wrong, then the complementary probability represents the probability that at least one is right.)

In a certain community, the probability that someone likes p…

In a certain community, the probability that someone likes piña coladas and getting caught in the rain is 0.03.  The probability that they like getting caught in the rain is 0.15. After selecting someone at random, we discover that they like getting caught in the rain.  Find the probability that they like piña coladas, given that they like getting caught in the rain. Write your answer in the form of a decimal number between 0 and 1. (Hint: P ( E | F ) = P ( E  and  F ) P ( F ) P(E|F) = \frac{P(E \text{ and } F)}{P(F)} .)