Question

Two fair dice are rolled 3 times and the sum of the numbers that come up is recorded. Find the probability of these events. a. The sum is 4 on each of the three rolls. b. The sum is 4 exactly twice in the three rolls. a. The probability the sum is 4 on each of the three rolls is nothing. ​(Type an integer or a simplified​ fraction.)

Answer 1

Explanation:

Given that two fair dice are rolled 3 times and the sum of the numbers that come up is recorded.

a) The sum is 4 on each of the three rolls.

(1,3) (2,2) (3,1) HEnce for one throw prob = 3/36 =1/12

Prob for getting same sum 4 in 3 rolls =
`((1)/(12) )^3`

(since each trial is independent)

b) Prob sum =4 in exactly 2 rolls

=
`3C2 (1/12)^2 (11/12)`=
`(33)/(12^3)`