Question

A student is applying to Harvard and Dartmouth. He estimates that he has a probability of .5 of being accepted at Dartmouth and .3 of being accepted at Harvard. He further estimates the probability that he will be accepted by both is .2. What is the probability that he is accepted by Dartmouth if he is accepted by Harvard? Is the event “accepted at Harvard” independent of the event “accepted at Dartmouth”?

Answer 1

draw a tree diagram according to this the probability of first accepted by Harvard (H) multiplied by the probability of accepted by Dartmouth (D) is simply 0.15. Logically speaking these two events should be independent but this does not seem to be the case here.