Chapter 12, Problem 17CT

To determine

Find the probability of choosing $2Y\text{'}s$ .

Answer to Problem 17CT

  $\frac{1}{9}$

Explanation of Solution

Given information:

Given: A bag contains $5X\text{'}S,4Y\text{'}Sand3Z\text{'}s$ tiles. You replace the first tile in the bag and choose again.

Calculation:

Here, the total no. of tiles in the bag is $12$ .

  $\begin{array}{l}P\left(event\right)=\frac{numberoffavorableoutcomes}{numberofpossibleoutcomes}\\ P\left(Y\right)=\frac{4}{12}\\ P\left(Y\right)=\frac{1}{3}\\ Now,\\ P\left(YandY\right)=P\left(Y\right).P\left(Y\right)\\ P\left(YandY\right)=\frac{1}{3}.\frac{1}{3}\\ P\left(YandY\right)=\frac{1}{9}\end{array}$

Hence, the required answer is $\frac{1}{9}$ .