Determine the value of each binomial coefficient.

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**2. Craps.**The game of craps is played by rolling two
balanced dice. A first roll of a sum of 7 or 11 wins; and a first roll
of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum
must be repeated before a sum of 7 is thrown. It can be shown that the
probability is 0.493 that a player wins a game of craps. Suppose we
consider a win by a player to be a success,*s*.

**a.**Identify the success probability,*p*.

**b.**Construct a table showing the possible win–lose
results and their probabilities for three games of craps. Round each
probability to three decimal places.

**c.**Draw a tree diagram for part (b).

**d.**List the outcomes in which the player wins exactly two out of three times.

**e.**Determine the probability of each of the outcomes in part (d). Explain why those probabilities are equal.

**f.**Find the probability that the player wins exactly two out of three times.

**g.**Without using the binomial probability formula, obtain the probability distribution of the random variable*Y*, the number of times out of three that the player wins.

**h.**Identify the probability distribution in part (g).