Multiple choice

A bag contains three white, two black and four red balls. If four balls are drawn at random with replacement, the probability that the sample contains just one white ball is

  1. $\displaystyle \frac { 32 }{ 81 } $
  2. $\displaystyle \frac { 11 }{ 2 } $
  3. $\displaystyle \frac { 32 }{ 93 } $

  4. None of these
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A Correct answer
Explanation

Total balls = 9. P(White) = 3/9 = 1/3. P(Not White) = 2/3. For 4 draws with replacement, P(1 white) = 4C1 * (1/3)^1 * (2/3)^3 = 4 * (1/3) * (8/27) = 32/81.

AI explanation

The bag has 9 balls, so the probability of drawing a white ball is 3/9 = 1/3 and the probability of drawing a non-white ball is 2/3. Using the binomial distribution formula for exactly 1 success in 4 trials, we calculate P(1) = 4C1 x (1/3)^1 x (2/3)^3. This gives 4 x (1/3) x (8/27), which equals 32/81.

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