Multiple choice

There are three bags, $B_{1}, B_{2}$ and $B_{3}$ containing $2$ Red and $3$ White, $5$ Red and $5$ White, $3$ Red and $2$ White balls respectively. A ball is drawn from the bag $B_{1}$ and placed in bag $B_{2}$ then a ball is drawn from bag $B_{3}$. Find the probability that both the drawn ball is white

  1. $\dfrac{2}{25}$
  2. $\dfrac{3}{25}$
  3. $\dfrac{4}{25}$
  4. $\dfrac{6}{25}$
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D Correct answer
AI explanation

The probability of drawing a white ball from bag B1 is 3/5, which would leave 6 white and 5 red balls in bag B2, giving a 6/11 chance of drawing a white ball from B2. The probability of drawing a red ball from B1 is 2/5, which would leave 5 white and 6 red balls in B2, giving a 5/11 chance of drawing a white ball from B2. However, the problem states the second ball is drawn from bag B3, which has a fixed probability of 2/5 for drawing a white ball. Using the multiplication rule for independent events, the probability that the ball from B1 is white AND the ball from B3 is white is (3/5) * (2/5) = 6/25.

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