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Yоu hаve аpplied tо twо different universities, the U of A аnd the U of B, for graduate school. In the past, U of A has accepted 32% of students who have applied with similar credentials as yours,while U of B has accepted 35% of students who have applied with similar credentials as yours. Because these are two separate universities, you should assume that the decision of each university to accept you or not is independent of each other. (Provide your answers to 3 decimal places.) (1) What is the probability that you will be accepted in both universities? [both] (2) What is the probability that you will be accepted into the U of A or the U of B? [Or] (3) What is the probability that one but only one of these two universities will accept you? [only1] (4) What is the probability that you do not get into either university? [Neither] (5) Given that you are accepted first into the U of A, what is the probability that you are then accepted into the U of B? [Afirst]
In the finаl rоund оf а TV gаme shоw, contestants have a chance to increase their current winnings of $500,000 to $1 million. If they are wrong, their prize is decreased to $250,000. The contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?