There are five black cats and four 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?

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Answer 1 · 2016-10-03T12:51:03

#P(G,G) = 1/6#

This is a situation of dependent probability.
The probability of the second event depends on the outcome of the first event.

To have 2 gray cats escaping, means the First one is gray AND the second is gray:

As each cat escapes, the number of cats changes.

There are 9 cats, 4 of which are gray #P(G) = 4/9#

#P(G,G) = P(G) xx P(G)#

#P(G,G) = 4/9 xx3/8" "larr# there are then 8 cats, only 3 are gray

#P(G,G) = cancel4/cancel9^3 xxcancel3/cancel8^2 = 1/6#

#P(G,G) = 1/6#