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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.

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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?
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APPEARS IN

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