Question

There are 3 black cats and 6 gray cats in a cage. The cage door opens and 2 cats escape. What is the probability that both cats that escaped are gray? Give answer as a percentage.

Answer 1

42%

Explanation:

You want to know the probability that two cats from a group of 6 gray and 3 black cats are both gray.

Outcomes

There are a total of 9C2 = 36 possible pairs of cats in a group of 9 cats. If 6 of them are gray, there are 6C2 = 15 pairs of gray cats in the group.

The probability that both of 2 cats from a group of 9 are gray is ...

15/36 ≈ 0.4167 ≈ 42%

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Additional comment

nCk is the number of ways k items can be chosen from a group of n. Its value is ...

nCk = n!/(k!(n -k)!)

9C2 = 9·8/2 = 36

6C2 = 6·5/2 = 15

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