A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is

Question

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is (A) 1 / 15 (B) 2 / 5 (C) 4 / 15 (D) 7 / 15

Tardigrade Admin · Accepted Answer

The number of ways to select 2 balls out of 10= 10 C2 Number of ways to select 2 balls both white = 6 C2 Number of ways to select 2 balls both black = 4 C2 ∴ The required probability =( 6 C2+ 4 C2/ 10 C2)=(7/15)

Q. A bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour, is

1 / 15

2 / 5

4 / 15

7 / 15

The number of ways to select $2$ balls out of
$10 =^{10} C_{2}$
Number of ways to select $2$ balls both white $=^{6} C_{2}$
Number of ways to select $2$ balls both black $=^{4} C_{2}$
$∴$ The required probability
$= \frac{^{6} C _{2} + ^{4} C _{2}}{^{10} C _{2}} = \frac{7}{15}$

Q. A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is