Question

Two boxes are containing 20 balls each and each ball is either black or white. The total number of black ball in the two boxes is different from the total number of white balls. One ball is drawn at random from each box and the probability that both are white is 0.21 and the probability that both are black is k, then `(100"k")/13` is equal to ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Two boxes are containing 20 balls each and each ball is either black or white. The total number of black ball in the two boxes is different from the total number of white balls. One ball is drawn at random from each box and the probability that both are white is 0.21 and the probability that both are black is k, then `(100"k")/13` is equal to 2.00.

Explanation:

Let first box has exactly a and the other has exactly b white balls.

⇒ `"a"/20."b"/20 = 21/100`

⇒ ab = 84

⇒ (a, b) is either (6, 14) or (7, 12), (14, 6), (12, 7)

But (6, 14) and (14, 6) is not possible

∵ a + b ≠ 20

⇒ (a, b) is (7, 12) or (12, 7)

⇒ P(both drawn balls are black)

= `13/20 xx 8/20`

= 0.26

= k

Now, `(100"k")/13 = (100 xx 0.26)/13` = 2.00