# Two Balls Are Drawn at Random with Replacement from a Box Containing 10 Black and 8 Red Balls. Find the Probability that - Mathematics

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that

(i) both balls are red.

(ii) first ball is black and second is red.

(iii) one of them is black and other is red.

#### Solution

Total number of balls = 18

Number of red balls = 8

Number of black balls = 10

(i) Probability of getting a red ball in the first draw = 8/18 = 4/9

The ball is replaced after the first draw.

∴ Probability of getting a red ball in the second draw = 8/18 = 4/9

Therefore, probability of getting both the balls red = 4/9 x 4/9 = 16/81

(ii) Probability of getting first ball black = 10/18 = 5/9

The ball is replaced after the first draw.

Probability of getting second ball as red = 8/18 = 4/9

Therefore, probability of getting first ball as black and second ball as red =5/9xx4/9 = 20/81

(iii) Probability of getting first ball as red =8/18 = 4/9

The ball is replaced after the first draw.

Probability of getting second ball as black =10/18 = 5/9

Therefore, probability of getting first ball as black and second ball as red = 4/9 xx 5/9 = 20/81

Therefore, probability that one of them is black and other is red

= Probability of getting first ball black and second as red + Probability of getting first ball red and second ball black

= 20/81 + 20/81

= 40/81

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 12 Maths
Chapter 13 Probability
Q 13 | Page 547