Question

A bag contains $3$ black and $4$ white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white

• A. $\frac{4}{49}$
• B. $\frac{1}{7}$
• C. $\frac{4}{7}$
• D. $\frac{12}{49}$

Answer 1

The correct option is C

$\frac{4}{7}$

Explanation for the correct option:

Find the probability that the second drawn ball is white:

Total number of balls in the bag $=3+4$

$=7$

The second white ball can be drawn in two different ways

First is black and second is white:

In this case the probability $=\frac{3}{7}\times \frac{4}{6}$

$=\frac{2}{7}$

First is white and second is white:

In this case the probability $=\frac{4}{7}\times \frac{3}{6}$

$=\frac{2}{7}$

$\therefore$The probability that the second drawn ball is white $=\frac{2}{7}+\frac{2}{7}$

$=\frac{\mathbf{4}}{\mathbf{7}}$

Hence, option ‘C’ is Correct.