Joe and Mimi are pen pals who exchange letters. When Mimi receives a letter from

Question

Joe and Mimi are pen pals who exchange letters. When Mimi receives a letter from Joe, she may or may not answer him, depending on her mood. If she is in a good mood, then the probability that she will answer is .80. Otherwise, the probability she will answer is .20. Mimi is in a good mood 30% of the time. Each time a letter is sent in the mail, there is a probability of .04 that it will get lost and never arrive. If Joe sends a letter to Mimi, what is the probability that he willl receive an answer from her?

Explanation / Answer

probability of receving answer = probability that letter sent successfully * proability that she was in good mood * probability that she will reply. + probability that letter sent successfully * proability that she was in not good mood * probability that she will reply in bad mood. probability that letter sent successfully = 0.96 (0.04 lost probability) proability that she was in good mood = 0.3 (30%) probability that she will reply. = 0.8 proability that she was in not good mood = 0.7 (1-0.3) probability that she will reply in bad mood. = 0.2 now probability of receving answer = 0.96*0.3*0.8 + 0.96*0.7*0.2 = 0.3648 so there is 36 % chance of receving the answer from her.

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