If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn, is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: A
Solution
The favorable cases for "2 white, 1 black" are three scenarios based on which box contributes the black ball.
Case 1: Black from Box 1, White from Box 2, White from Box 3:
(1/4)(2/4)(1/4) = 2/64
Case 2: White from Box 1, Black from Box 2, White from Box 3:
(3/4)(2/4)(1/4) = 6/64
Case 3: White from Box 1, White from Box 2, Black from Box 3:
(3/4)(2/4)(3/4) = 18/64
Total probability = (2 + 6 + 18)/64 = 26/64 = 13/32.
Case 1: Black from Box 1, White from Box 2, White from Box 3:
(1/4)(2/4)(1/4) = 2/64
Case 2: White from Box 1, Black from Box 2, White from Box 3:
(3/4)(2/4)(1/4) = 6/64
Case 3: White from Box 1, White from Box 2, Black from Box 3:
(3/4)(2/4)(3/4) = 18/64
Total probability = (2 + 6 + 18)/64 = 26/64 = 13/32.
[1998]