Question

A biased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6 turning up is the same . If three such dice are rolled, what is the probability of getting a sum of at least 14 without getting a 6 on any die ?

Option 1 : 5/24
Option 2 : 9/160
Option 3 : 1/30
Option 4 : 7/160

Answer 1

Possibilities of outcomes:
5, 5, 5
5, 5, 4

P(sum at least 14) = P(5,5,4) + P(5,5,5)
= 1/4 x 1/4 x 3/20 + 1/4 x 1/4 x 1/4
1/40