Chapter 12.8, Problem 35PPE

To determine

To find: The probability that an apple drink and then a citrus drink are handed out.

Answer to Problem 35PPE

The required probability is $\frac{3}{22}$ .

Explanation of Solution

Given:

There are 5 citrus drinks, 3 apple drinks, and 3 raspberry drinks.

Calculation:

Find the probability that 3 apple drinks out of 11 drinks.

  $P\left(\text{apple}\right)=\frac{3}{11}$

Find the probability that 5 citrus drinks out of the remaining 10 drinks.

  $\begin{array}{c}P\left(\text{citrus}\text{after}\text{apple}\right)=\frac{5}{10}\\ =\frac{1}{2}\end{array}$

Find the required probability as follows.

  $\begin{array}{c}P\left(\text{apple}\text{then}\text{citrus}\right)=P\left(\text{apple}\right)\times P\left(\text{citrus}\text{after}\text{apple}\right)\\ =\frac{3}{11}\times \frac{1}{2}\\ =\frac{3}{22}\end{array}$

Therefore, the required probability is $\frac{3}{22}$ .