Multiple choice

A bag contains $2$ white, $3$ black and $4$ green balls.Two balls are drawn one after another with replacement.The probability that the first one is white and the second one is black is

  1. $\displaystyle \frac{5}{27}$
  2. $\displaystyle \frac{1}{9}$
  3. $\displaystyle \frac{2}{27}$
  4. $\displaystyle \frac{4}{27}$
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C Correct answer
Explanation

Total balls = 2 + 3 + 4 = 9. Probability of white = 2/9. Probability of black = 3/9 = 1/3. Since the draw is with replacement, the events are independent: (2/9) * (3/9) = 6/81 = 2/27.

AI explanation

Since the balls are drawn with replacement, the two drawings are independent events and their probabilities multiply. The probability of drawing a white ball first is 2 divided by the total of 9 balls, which equals 2/9. The probability of subsequently drawing a black ball is 3 divided by 9, which equals 1/3. Multiplying these independent probabilities gives (2/9) * (1/3), which equals 2/27.

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