Simulating the Roll of One Die Can

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 six chance of rolling that number, then adding it to the amount of times a three can be rolled or a six can be rolled would tell us that the probability of losing would be four out of thirty six (total rolls that a 2, 3 or 12 can be thrown).

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.

================ 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. The law of averages is a myth; when students looked at the three available sequences they determined that the dice turned up red, then green,.