Question

12 #3

Find the probability of throwing a sum of 6 at least 4 times in 6 throws of a pair of fair dice.

Answer 1

First we will have to obtain the probability of getting a sum of six while throwing a pair of die

Number of Total cases = 6^2 = 36

Number of cases of getting 6 = { (1,5), (2,4), (3,3), (4,2), (5,1) } = 6

P[ getting a sum of six while throwing a pair of die ] = 6/36

P[ getting a sum of six while throwing a pair of die ] = 1/6

For the further part we can use binomial

with n = 6, x = 4 and p = 1/6 = 0.16667

The population proportion of success is p = 0.16667 , also, 1 - p = 1 - 0.16667 = 0.83333 , and the sample size is n= 6n=6. We need to compute

Therefore, we get that

This implies that

which means that the probability we are looking for is