# A bag contains 1 red ball and 2 white balls. One ball is randomly selected from the bag and then returned. What is the probability that exactly one of the first five balls selected is white?

Jan 14, 2017

The answer is $= \frac{10}{243}$

#### Explanation:

This is a binomial distribution.

The probability of getting 1 white ball on one draw is ${P}_{w} = \frac{2}{3}$

The probability of not getting a white ball on one draw$= 1 - {P}_{w} = \frac{1}{3}$

The probability of getting 1 white ball on the five draws is

$= \left(\begin{matrix}5 \\ 1\end{matrix}\right) \cdot \left(\frac{2}{3}\right) \cdot {\left(\frac{1}{3}\right)}^{4}$ where

((5),(1))=(5!)/((5-1)!(1!))=5

Therefore,

$P$(1 out of 5) $= 5 \cdot \frac{2}{3} \cdot {\left(\frac{1}{3}\right)}^{4} = \frac{10}{243}$