Question

# Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that  both balls are red.   Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that  first ball is black and second is red.  Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability. that   one of them is black and other is red

Solution

## Total number of balls = 18, number of red balls = 8 and number  of black balls = 10   ∴  Probability of drawing a red ball Number of red ballsTotal number of balls=818  Similarly , probability of drawing a black ball = Number of black ballsTotal number of balls=1018  Probability of getting both red balls = P (both balls are red) = P (a red ball is drawn at first draw and again a red ball at second draw) =818×818=1681 Total number of balls = 18, number of red balls = 8 and number  of black balls = 10   ∴  Probability of drawing a red ball Number of red ballsTotal number of balls=818  Similarly , probability of drawing a black ball = Number of black ballsTotal number of balls=1018  P (probability of getting first ball is black and second is red) =1018×818=2081 Total number of balls = 18, number of red balls = 8 and number  of black balls = 10   ∴  Probability of drawing a red ball Number of red ballsTotal number of balls=818  Similarly , probability of drawing a black ball = Number of black ballsTotal number of balls=1018 Probability of getting one black and other red ball = P (first ball is black and second is red) + P (first ball is red and second is black) =1018×818+818×1018=4081

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