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Three balanced coins are tossed independently. One of the variables of interest is Y1, the number of heads. Let Y2 denote the amount of money won on a side bet in the following manner. If the first head occurs on the first toss, you win $1. If the first head occurs on toss 2 or on toss 3 you win $2 or $3, respectively. If no heads appear, you lose $1 (that is, win -$1).
a Find the joint probability function for Y1 and Y2.
b What is the probability that fewer than three heads will occur and you will win $1 or less?
A raffle offers a first prize of $1000 2 second prizes of $300 and 20 third prizes of $10 each. If 15000 tickets are sold at 75 cents each, find the expected winnings (IN CENTS) for a person buying one ticket?
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