# Probability using Random number generation - Statistics Probability by ClassOf1

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A common dice game problem - Probability.

• pg 1
```									              Sub: Statistics                                                                           Topic: Probability

Question:
Find the Probability using random number generation.
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A common dice game called craps is played in several variations, resulting in an infinitely large
probability tree. To see some of the results associated with large probability trees, consider the
following single die game, similar to craps, which we will call scraps.

A player rolls a single die, if the player rolls 2 or 6, he wins. If the player rolls a 1 he loses. With
any other result the player rolls again. If his second roll matches his first roll, he wins. If the 2nd
roll is 1, 2, or 6, he loses. If the player does not win or lose on his second roll he continues to
roll, using the same criteria given for the second roll.

i.e. 6 wins

3 4 6 loses

1 loses

3 5 2 loses

3 5 4 3 wins

3 3 wins

2 wins

5 3 3 3 3 4 5 wins

1. Play 100 games of scraps and empirically determine an estimate for the probability of
winning.

2. Using classical methods discussed in class, try to estimate the probability of winning. (You will
likely not be able to get this exactly because of the nature of the problem, just make the best
estimate you can)

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Sub: Statistics                                                                           Topic: Probability

3. How close is the calculated value to your experimental value?

Solution:

1. Play 100 games of scraps and empirically determine an estimate for the probability of
winning.

The 100 games of scraps were played using EXCEL. Steps to be followed in Excel are as follows:

 Click ‘Data’ on the main menu. Then select ‘Data Analysis’.
 Click ‘Random number generation’.
 Enter ‘1’ in the number of variables and ‘1’ in the number of random numbers. Select
the distribution as ‘discrete’. Then enter the range of the following table in the
probability input range:
Value      Probability

1        0.166667

2        0.166667

3        0.166667

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