## Book: Mathematics Part-II

### Chapter: 13. Probability

#### Subject: Maths - Class 12th

##### Q. No. 13 of Exercise 13.2

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13
##### 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.

Given: A box containing 10 black and 8 red balls.

Total number of balls in box = 18

(i) both balls are red.

Probability of getting a red ball in first draw = As the ball is replaced after first throw,

Hence, Probability of getting a red ball in second draw = Now, Probability of getting both balls red = (ii) first ball is black and second is red.

Probability of getting a black ball in first draw = As the ball is replaced after first throw,

Hence, Probability of getting a red ball in second draw = Now, Probability of getting first ball is black and second is red = (iii) one of them is black and other is red.

Probability of getting a black ball in first draw = As the ball is replaced after first throw,

Hence, Probability of getting a red ball in second draw = Now, Probability of getting first ball is black and second is red = Probability of getting a red ball in first draw = As the ball is replaced after first throw,

Hence, Probability of getting a black ball in second draw = Now, Probability of getting first ball is red and second is black = Therefore, Probability of getting one of them is black and other is red :

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

= 13

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