There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance. Find the probability of the following selection. P(2 black haired children)

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30-11-2016
Mathematics

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There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance. Find the probability of the following selection. P(2 black haired children)

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JcAlmighty JcAlmighty · Answer 1 · 2016-12-05T20:16:42+01:00

The answer is 7/69.

There are 8 black-haired children among 24 children. The probability of randomly selecting black haired children for the first time is:
P1 = 8/24 = 1/3

Now, there are 7 black-haired children left among 23 children. The probability of randomly selecting black haired children for the second time is:
P2 = 7/23

Since we want both of these events to occur together, we will multiply their probabilities:
P = P1 * P2 = 1/3 * 7/23 = 7/69