Question

A bag contains $4$white and $3$red balls. Two draws of one ball each are made without replacement. That the probability that both the balls are red is

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{4}{7}$

Answer 1

The correct option is A

$\frac{1}{7}$

The explanation for the correct option:

Step 1: The given data:

Number of white balls = $4$

Number of red balls = $3$

In the first draw, a ball is drawn.

So total number of balls $=3+4$

$=7$

In the second draw, the ball is not replaced.

So total number of balls $=7-1$

$=6$

Step 2: Finding the probability:

Thus, the probability that both the balls are red

$$\begin{gathered} =\frac{{}^{3}C_1}{{}^{7}C_1}\times \frac{{}^{2}C_1}{{}^{6}C_1} \\ =\frac{3}{7}\times \frac{2}{6} \\ =\frac{1}{7} \end{gathered}$$

Hence, option (A) is the correct answer.