Chapter 12, Problem 18CT

To determine

Find the probability of choosing $2bluemarbles$ .

Answer to Problem 18CT

  $\frac{1}{35}$

Explanation of Solution

Given information:

Given: A bag contains $3blue,5yellow,7redmarbles$ . You choose a second marble without replacing the first.

Calculation:

Here, the total number of balls present in the bag is $15$ .

  $\begin{array}{l}P\left(event\right)=\frac{numberoffavorableoutcomes}{numberofpossibleoutcomes}\\ P\left(bluemarble\right)=\frac{3}{15}\\ P\left(bluemarble\right)=\frac{1}{5}\\ Now,\\ P\left(bluemarbleafterbluemarble\right)=\frac{2}{14}\\ P\left(bluemarbleafterbluemarble\right)=\frac{1}{7}\\ P\left(bluemarbleafterbluemarble\right)=\frac{1}{5}.\frac{1}{7}\\ P\left(bluemarbleafterbluemarble\right)=\frac{1}{35}\end{array}$

Hence, the required answer is $\frac{1}{35}$ .