Chapter 12.5, Problem 13PPS

To determine

To state whether the probability is dependent or independent and find the probability.

Answer to Problem 13PPS

The events are dependent and the probability of both Chuck and Rashid choosing dry food is $\frac{5}{19}\text{ or 26}\text{.3\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Chuck and Rashid went to a pet store to buy dog food. They chose from $10$ brands of dry food, $6$ brands of canned food and $3$ brands of pet snacks. What is the probability that both choose dry food, if Chuck randomly chose first and liked the first brand he picked up?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The outcome of one event affects the outcome of the other because the food brand is not replaced, so they are dependent events.

The probability can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{Chuck choosing dry food}\right)=\frac{10}{19}\\ \text{P}\left(\text{Rashid choosing dry food}\right)=\frac{9}{18}\\ \text{P}\left(\text{Both choosing dry food}\right)=\frac{10}{19}\times \frac{9}{18}\\ \text{P}\left(\text{Both choosing dry food}\right)=\frac{5}{19}\text{ or 26}\text{.3\%}\end{array}$

Hence, the events are dependent and the probability of both Chuck and Rashid choosing dry food is $\frac{5}{19}\text{ or 26}\text{.3\%}$ .