Chapter 14.3, Problem 46STP

To determine

The probability that the first pencil will be yellow and the second pencil will be green.

Answer to Problem 46STP

The probability will be $\frac{1}{4}$ and the correct option will be B.

Explanation of Solution

Given:

A teacher is distributing the 15 yellow and 10 green pencils.

The options are given as:

  $\begin{array}{l}A\frac{1}{24}C\frac{2}{5}\\ B\frac{1}{4}D\frac{23}{25}\end{array}$

The total number of the pencils will be:

  $\begin{array}{l}=15+10\\ =25\end{array}$

Probability of the selection of the one yellow pencil from the total pencils:

  $P\left(y\right)=\frac{15}{25}$

Similarly, the probability of the green pencils from the remaining will be:

  $P\left(g\right)=\frac{10}{24}$

Now, evaluating the probability that the first pencil drawn is yellow and the second pencil is green:

  $\begin{array}{c}P=P\left(y\right)\times P\left(g\right)\\ =\frac{15}{25}\times \frac{10}{24}\\ =\frac{1}{4}\end{array}$

Therefore, the correct option is B.