Bring home a Diamond

Probability Level 3

A contestant on the game show "A Diamond for your Wife" gets to select 5 diamonds from a box. The box contains 20 diamonds of which 8 are fakes.

Regardless of how many real diamonds the contestant has after his selection, he can only take one home to his wife. A second contestant then gets to select from the remaining 15 diamonds in the box but he can select only 1.

What is the probability that this second contestant selects a real diamond?


The answer is 0.6.

Vishwa Shah by Vishwa Shah , 24, India

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2 solutions

Ivan Koswara
May 22, 2014

Note that whatever the first contestant does doesn't affect the second contestant, considering we don't know his result. (If we know his result, for example he successfully brings a real diamond home, then things get complicated with conditional probabilities.) Thus the answer is simply the number of diamonds in the box divided by the total number of diamonds: 12 20 = 0.6 \frac{12}{20} = 0.6 .

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Nathan Ramesh
May 22, 2014

The expected number of real diamonds the first contestant takes is 8 20 ⋅ 5 = 2 \dfrac{8}{20}\cdot 5=2 and the expected number of real diamonds he takes is 12 20 ⋅ 5 = 3 \dfrac{12}{20}\cdot 5=3 so we have 12 − 3 20 − 5 = 0.6 \dfrac{12-3}{20-5}=\boxed{0.6}

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