Question

Two balls are drawn at random, with replacement from a box containing 9 black and 7white balls. Calculate the probability of both balls are black.​

Answer 1

Given the total number of black balls = 10 and total number of red balls = 8.

P (drawing a black ball) = 1018=59 and P (drawing a red ball) = 818=49

(i) P (both balls are red):

P (both balls are red) = P (a red is drawn first and a red is drawn second time also) = P (drawing a red) × P (drawing a red) = 49 × 49 = 1681

(ii) P (first ball is black and second is red):

P (first ball is black and second is red) = P (drawing a black first) × P (drawing a red) = 59 × 49 = 2081

(iii) P (getting one black and one red ball):

P (getting one black and one red ball) = P (first ball is black and second is red) + P (first ball is red and second is black)

We calculated the P (drawing a black ball first and red second above) in (ii). The P (drawing a red first and black second) is also the same.

Therefore, P (getting one black and one red ball) = 2081+ 2081=4081

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