Pair of Dice Roll a pair of dice 60 times and record the sum

Pair of Dice. Roll a pair of dice 60 times and record the sums. Determine the empirical probability of rolling a sum of

a) 2.

b) 7.

c) Does the probability of rolling a sum of 2 appear to be the same as the probability of rolling a sum of 7? Explain your answer.

Solution

Well, the empirical probabilities actually require you to roll the dice. Theoretically, there is one way of getting a sum of 2. That is, roll 1 twice. This has a probability of 1/36 or about 0.02778.

On the other hand, one can roll a 7 in the following ways. (1, 6) or (6, 1) or (2, 5) or (5, 2) or (3, 4) or (4, 3). Thus, the probability of getting a sum of 7 should be about 7/36 or 0.1944.

Let\'s see if I get something like this...

The empirical probability for 2 is 2/60 or 1/30 or 0.033.

The empirical probability for 7 is 11/60 or 0.1833.

c. The probabilities certainly appear different, as expected.