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1. A fair coin is thrown n times. Show that the conditional probability of a head on any specified trial, given a total of k heads over the n trials, is k/n (k > 0).

2. (Johnsonbough8) A coin with probability p for heads is tossed n times. Let E be the event "a head is obtained on the first toss' and Fk the event ‘exactly k heads are obtained." For which pairs (n, k) are E and Fk independent?

3. Suppose that A and B are events such that P (A|B) = P (B|A) and P (A∪B) = 1 and P (A ∩ B) > 0. Prove that P (A) > 1/2.

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