Multiple choice

Three boxes contain respectively $3$ white and $1$ black, $2$ white and $2$ black, $1$ white and $3$ black balls, from each of the boxes one ball is drawn at random. The probability that $2$ white and $1$ black balls will be drawn is

  1. $\dfrac {13}{32}$
  2. $\dfrac {1}{4}$
  3. $\dfrac {1}{32}$
  4. $\dfrac {3}{16}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The three possible arrangements are WWB, WBW, and BWW. Their probabilities are 9/32, 3/32, and 1/32, respectively, giving a total of 13/32.

AI explanation

The probabilities of drawing a white ball from the first, second, and third boxes are 3/4, 2/4, and 1/4 respectively. To draw 2 white and 1 black ball, we calculate the sum of three scenarios: white from the first two and black from the third, white from the first and third and black from the second, and black from the first and white from the last two. This calculates to (3/4 * 2/4 * 3/4) + (3/4 * 2/4 * 1/4) + (1/4 * 2/4 * 1/4) = 18/64 + 6/64 + 2/64 = 26/64 = 13/32.

Keep practicing — related questions