Difficult# 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?