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    Suppose you are eating at a pizza parlor with two friends. You have agreed to the following rule about who will pay the bill: Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all three tosses yield the same result, the bill will be shared by all. Find the probability that:

    a) Only you will have to pay.
    b) All three will share.

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    Solution Preview

    Let A = event that Friend 1 gets a head
    Let B = event that Friend 2 gets a head
    Let C = event that I get a head
    Now P(A) = P(B) = P(C) = P(A') = P(B') = P(C') = 0.5

    (a) If ...