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Find the probability that the player wins a game of craps.
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Answer to Problem 138E
The probability that the player wins a game of craps is 0.4929.
Explanation of Solution
Calculation:
Let A denote the
The possible outcomes when rolling two dice are shown below:
The formula for finding the probability that the player wins a game of craps is shown below:
From the given information,
Also,
For k = 4, 5, 6, 8, 9 and 10,
Here, the tosses are independent.
Let Fk denote the event that player do not throw a k or a 7, for k =4, 5, 6, 8, 9, 10.
The Event Ck is obtained as follows:
The probability of C4 is obtained as given below:
Similarly, the probabilities of
From the sample outcomes, it can be observed that,
Therefore,
The probability that the player wins a game of craps is obtained as follows:
Thus, the probability that the player wins a game of craps is 0.4929.
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Mathematical Statistics with Applications
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