Please answer all parts of the question and all work shown. Suppose a professor of probability is tired of reading the depressi
Please answer all parts of the question and all work shown.
Suppose a professor of probability is tired of reading the depressing news and so he decides that he will quickly scan the first 5 headlines in the New Yorks Times and the first 5 headlines in the Boston Globe and if at most 3 of the articles in each are depressing, he will read the news that day. Further suppose that the probability of a NYTs headline being depressing is 0.6 and for the Globe the probability of a headline being depressing is 0.55.
(a) What is the probability that he will read the news the first day he tries this?
(b) In order to be “well-informed” he needs to read the news at least half the time; what is the probability that he will be well-informed after doing this for a week?
Hint: This is another problem where there are two independent parts of the random experiment. You might want to phrase it as three different random variables, all three binomial.