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

Answer:

Step-by-step 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 = $(\frac{1}{12} )^3$

(since each trial is independent)

b) Prob sum =4 in exactly 2 rolls

= $3C2 (1/12)^2 (11/12)$=$\frac{33}{12^3}$