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

Answer:

$E(x) = 1.5$

Step-by-step 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:

$p= \frac{1}{6}$ ---- the theoretical probability of rolling 2

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

$E(x) = np$

$E(x) = 9 * \frac{1}{6}$

$E(x) = \frac{9}{6}$

Simplify

$E(x) = \frac{3}{2}$ or

$E(x) = 1.5$