Simulating the roll of one die can be accomplished by knowing that it can only fall one of six ways. Each roll means that a certain number on the die has 1/6 of a chance of turning up. The probability of that number showing up is therefore 1/6 each time the die is cast. In the game of craps however, there are two dice being thrown each time. Using two dice changes things dramatically. Now, instead of a single number showing up 1/6 of the time, the probability that two different numbers show up increases to a certain number out of 36. Thirty six represents the numbers on both dice times each other (6 x 6). It is known that the number two can only come up in one manner (1 + 1) so, the probability of getting a sum of 2 is one out of a possible 36. One way to determine the chances of a sum showing up is through a simulation. To determine the probability of winning one must know the probablity of rolling a certain number. Since rolling a two is an automatic loser and there is a one out of thirty...

That means the thrower would lose 12.5% of the time on the first roll of the dice. A tree diagram showing four rolls of the dice displayed this scenario: Game
Sum on first roll
Result of first roll
Overall Result
1
5
point
point
2
8
none
none
3
7
none
lose
4
10
point
point
5




The probability of the player winning based on the four rolls turned out to be zero, since the player did not win.
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Explaining why sixty three percent of 260 students chose the second sequence of events is due to the fact that they did not know about the law of averages.…