Theory question 105
ProbabilityA 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.
Show the model answer
Model answer
Let n = number of silver marbles; total = n + 7
n/(n + 7) × (n − 1)/(n + 6) = 1/15
15n² − 15n = n² + 13n + 42 ⇒ 14n² − 28n − 42 = 0 ⇒ n² − 2n − 3 = 0
(n − 3)(n + 1) = 0 ⇒ n = 3 silver marbles
Explanation
Without replacement, the second fraction has one less on top and bottom.