This paper circulates around the core theme of Find the probability that the player wins exactly two out of three times.Without using the binomial probability formula, obtain the probability distribution of the random variableY, the number of times out of three that the player wins.Identify the probab together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 45. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.

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).