Question

Bob is taking a test. There are two questions he is stumped on and he decides to guess. Let A be the event that he gets the first question right; let B be the event he gets the second question right (adapted from Blom et al., 1991) (a) Obtain an expression for p, the probability that he gets both questions right conditional on getting the first question right |(b) Obtain an expression for p2, the probability that he gets both questions right conditional on getting either of the two questions right (A or B) (c) Show that p2 p1. This may seem paradoxical. Knowledge that A or B has taken place makes the conditional probability that A and B happens smaller than when we know that A has happened. Can you untangle the paradox?

Answer 1

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