Question

5. A basket contains 3 gold-plated marbles, 4 diamond marbles and some silver marbles, all of the same size and shape. Two marbles were drawn from the basket at random one after the other without replacement. If the probability that the two marbles were all silver is 1/15, find the number of silver marbles.

Accepted Answer

Let the number of silver marbles = s. Total marbles = 3+4+s = 7+s.
P(both silver, no replacement) = [s/(7+s)] × [(s−1)/(6+s)] = 1/15.
15s(s−1) = (7+s)(6+s)
15s²−15s = s²+13s+42
14s²−28s−42 = 0
Dividing by 14: s²−2s−3 = 0
(s−3)(s+1) = 0 → s = 3 (rejecting the negative root).
Number of silver marbles = 3.

NABTEB Mathematics 2024 Theory — Question 5

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