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AP® Statistics

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Simulating the Game of Craps

APSTAT-3EPBA4

The game of Craps is a casino game in which a player rolls a pair of $6$-sided dice. On the first roll of the dice, if the sum is $7$ or $11$, it is called a “natural” and the player wins. Sierra wants to try the game but wonders what the probability of a “natural” is.

Unfortunately, she is really bad at probability so she programs her computer to simulate $10,000$ tosses of a pair of dice and use the results to calculate the probability of a “natural”.

Which of the following would Sierra most likely conclude as a result of this simulation? Why?

A

Sierra will conclude that the probability of a “natural” is $0.001$. Although the true probability is $0.03$, $10,000$ simulations is not a sufficiently large number to predict the true probability with any degree of accuracy.

B

Sierra will conclude that the probability of a “natural” is $0.04$. The true probability is $0.06$ but $10,000$ simulations is not a sufficiently large number to predict the true probability with reasonable accuracy.

C

Sierra will conclude that the probability of a “natural” is $0.080$ because $10,000$ simulations is a sufficiently large number to predict the true probability with reasonable accuracy and the true probability is $0.083$.

D

Sierra will conclude that the probability of a “natural” is $0.113$ because $10,000$ simulations is a sufficiently large number to predict the true probability with reasonable accuracy and the true probability is $0.111$.

E

Sierra will conclude that the probability of a “natural” is $0.221$ because $10,000$ simulations is a sufficiently large number to predict the true probability with reasonable accuracy and the true probability is $0.222$.