(1) In each of the following scenarios, there is something wrong. Describe what is wrong and give a reason for your answer. (a) If the sample space consists of two outcomes, then each outcome has probability 0.5.
(b) If we select a digit at random, then the probability of selecting a 2 is 0.2.
(c) If the probability of A is 0.2, the probability of B is 0.3, and the probability of A and B is 0.5, then A and B are independent.
(2) An instant lottery game gives you probability
0.02 of winning on any one play. Plays are independent of each other. If you play five times, what is the probability that you win at least once?