Chapter 13, Problem 3SAP

To determine

To find: The number of green marbles that are needed to be added in the jar in order to double the probability of getting the green marble.

Answer to Problem 3SAP

The correct option is C.

Explanation of Solution

Given:

The number of red marble is 5, blue are 7 and the green are 3.

Calculation:

Consider the probability of the event is,

  $P=\frac{\text{number}\text{of}\text{favourable}\text{outcomes}}{\text{total}\text{outcomes}}$

Then, the favourable outcomes for getting green marble is,

  $\begin{array}{c}P=\frac{3}{5+7+3}\\ =\frac{3}{15}\end{array}$

Then, the probability of obtaining the green marble after adding the x marble is,

  $\begin{array}{l}\frac{3+x}{15+x}=\frac{6}{15}\\ 15x-6x=90-45\\ x=\frac{45}{9}\\ x=5\end{array}$

Thus, the correct option is C.