Question

Two fair dice are rolled 4 times and the sum of the numbers that come up are recorded. Find the probability of these events. A) the sun is 5 on each of the four rolls. B) the sun is 5 exactly three times in the four rolls.

Answer 1

See below in bold.

Explanation:

A. On one roll the possible ways to get a sum of 5 is (2,3, ) and (4, 1).

There are 36 possible outcomes from the one roll of the 2 dice.

So the probability of getting a sum of 5 on one roll = 2/36 = 1/18.

So the probability of 5 on 4 rolls = (1/18)^4

= 1/104976.

B.

The probability of the first 3 rolls being a 5 and the last one being not 5

= (1/18)^3 * (17/18)

= 17/104976

There are 4 ways to pick 3 out of 4 so the required probability

= 4 * 17/104976

= 68/104976.