Chapter 12.5, Problem 11PPS

To determine

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

Answer to Problem 11PPS

The events are dependent and the probability of choosing a milk chocolate and then a white chocolate is $\frac{5}{46}\text{ or 10}\text{.9\%}$ .

Explanation of Solution

Given information:

The given statement is:

“A box of chocolates contains $10$ milk chocolates, $8$ dark chocolates and $6$ white chocolates. Sung randomly chooses a chocolate, eats it, and then randomly chooses another. What is the probability that Sung choose a milk chocolate and then a white chocolate?”

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 chocolate is not replaced, so they are dependent events.

The probability that Sung chose a milk chocolate and then a white chocolate can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{milk chocolate}\right)=\frac{10}{24}\\ \text{P}\left(\text{white chocolate}\right)=\frac{6}{23}\\ \text{P}\left(\text{milk chocolate, white chocolate}\right)=\frac{10}{24}\times \frac{6}{23}\\ \text{P}\left(\text{milk chocolate, white chocolate}\right)=\frac{5}{46}\text{ or 10}\text{.9\%}\end{array}$

Hence, the events are dependent and the probability of choosing a milk chocolate and then a white chocolate is $\frac{5}{46}\text{ or 10}\text{.9\%}$ .