Question

A bowl contains 8 white marbles, 6 red marbles and 2 black marbles. Two marbles are drawn, without replacement.

Quantity A: The probability of both marbles drawn being white.
Quantity B: The probability of one marble being black from the two drawn.
A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

Answer 1

P(both marbles are white) = (8/16)(7/15)

= 7/30

P(one of the two marbles is black) =

(2/16)(8/15) + (8/16)(2/15) + (6/16)(8/15) +

(8/16)(6/15) =

1/15 + 1/15 + 1/5 + 1/5 = 8/15

Quantity B is greater.

The correct answer is B.