Chapter 11, Problem 15CR

To determine

To find the probability of drawing a blue marble and then another blue marble from a bag without replacing the first marble.

Answer to Problem 15CR

The probability of drawing a blue marble and then another blue marble from a bag without replacing the first marble is $\frac{18}{95}$ .

Explanation of Solution

Given information:

A bag has

  $5$ green, $6$ red and $9$ blue marbles.

Calculation :

Probability of drawing a blue marble, $\text{P}\left(\text{blue}\right)\text{=}\frac{9}{20}$

Probability of drawing another blue marble, without replacing the first, $\text{P}\left(\text{another blue}\right)\text{=}\frac{8}{19}$

  $\begin{array}{l}\text{P}\left(\text{blue and blue}\right)\text{=P}\left(\text{blue}\right)\cdot \text{P}\left(\text{another blue}\right)\\ \text{P}\left(\text{blue and blue}\right)=\frac{9}{20}\cdot \frac{8}{19}\left[\text{Substitute probabilities}\right]\\ \text{P}\left(\text{blue and blue}\right)=\frac{18}{95}\left[\text{Multiply}\right]\end{array}$

Hence, the probability of drawing a blue marble and then another blue marble from a bag without replacing the first marble is $\frac{18}{95}$ .