Chapter 13.4, Problem 6CFU

To determine

To find if each pair of events is independent or dependent and find the probability.

Answer to Problem 6CFU

Dependent, $\frac{2}{5}$

Explanation of Solution

Given:

The probability of randomly selecting two bottles from a cooler that contains $2$ bottles of fruit juice and $4$ bottles of sports drink.

Calculation:

The events are dependent because outcome of one event affects the outcome of another event.

Let A be the event of taking out $2$ bottles of fruit juice.

Let B be the event of taking out $4$ bottles of sports drink.

Total sample space $=6$

Therefore probability of event A is $P(A)=\frac{4}{6}=\frac{2}{3}$

Therefore probability of event B is $P(B)=\frac{3}{5}$

Hence,

  $\begin{array}{l}P(A\text{ and }B)=P(A)\times P(B)\\ P(A\text{ and }B)=\frac{2}{3}\times \frac{3}{5}=\frac{2}{5}\end{array}$