Question

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many​ times, find the mean for the number of twos.

Answer 1

`E(x) = 1.5\\`

Explanation:

Given

`n = 9` -- number of rolls

Required

The mean of 2's

The distribution follows binomial distribution where:

`X \to Binomial(n,p)`

In this case:

`p= (1)/(6)` ---- the theoretical probability of rolling 2

So, the mean of 2's is calculated using:

`E(x) = np`

`E(x) = 9 * (1)/(6)`

`E(x) = (9)/(6)`

Simplify

`E(x) = (3)/(2)` or

`E(x) = 1.5\\`