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There are three black cats and six gray cats in a cage, and none of them want to be in there the cage door opens briefly and two cats escape. What is the probability that both escaped cats are gray?

1 Answer

Dec 28, 2017

$\frac{5}{12}$ $5/12$

Explanation:

$total of 9 cats of which 6 are grey$ $"total of 9 cats of which 6 are grey"$

$P (grey) = \frac{6}{9} = \frac{2}{3}$ $P("grey")=6/9=2/3$

$there are now 8 cats of which 5 are grey$ $"there are now 8 cats of which 5 are grey"$

$P (grey) = \frac{5}{8}$ $P("grey")=5/8$

$\Rightarrow P (grey and grey) = \frac{2}{3} \times \frac{5}{8} = \frac{5}{12}$ $rArrP("grey and grey")=2/3xx5/8=5/12$

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