Multiple choice

A bag contains $3$ white, $2$ black and $4$ red balls.The probability of drawing a white, a black and a red ball in succession in that order without replacement is

  1. $\displaystyle \frac{8}{243}$
  2. $\displaystyle \frac{1}{21}$
  3. $\displaystyle \frac{5}{21}$
  4. $\displaystyle \frac{3}{21}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 9. Probability = (3/9) * (2/8) * (4/7) = (1/3) * (1/4) * (4/7) = 1/21.

AI explanation

The total number of balls initially in the bag is 3 white plus 2 black plus 4 red, which equals 9 balls. Using the multiplication rule for dependent events, the probability of drawing a white ball first is 3/9, then a black ball is 2/8, and finally a red ball is 4/7. Multiplying these probabilities gives (1/3) times (1/4) times (4/7), which equals 4/84. This simplifies to 1/21, meaning the required probability is 1/21.

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