Chapter 13, Problem 6SAP

To determine

To find: The probability of selecting the white marble.

Answer to Problem 6SAP

The correct option is E.

Explanation of Solution

Given:

The probability of selecting a blue marble is $\frac{1}{5}$ .

The bag contains 200 marbles.

The 100 white marbles added to the bag.

Calculation:

Consider the probability of the event is,

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

Then, the probability of getting the blue marble is,

  $\frac{1}{5}$

The bag contains the white and the blue marbles and the event of getting the white marble is complementary event of getting white marble is,

  $1-\frac{1}{5}=\frac{4}{5}$

Consider that the bag has 200 marbles then the number of blue marble is,

  $\frac{1}{5}\left(200\right)=40$

Thus, the number of marble is,

  $\frac{4}{5}\left(200\right)=160$

Consider that another 100 white marble is added to the bag, now the bag contains 260 white marbles and the 40 blue marbles.

Thus, the probability of the getting the white marble is,

  $\begin{array}{c}P=\frac{260}{300}\\ =\frac{13}{15}\end{array}$

Thus, the correct option is E.