Probability Question

Question

 

An animal cage is holding 6 black cats and 7 white cats. All of them want to get out of the cage. The cage door is opened slightly and two cats escape. What is the probability that a black cat is followed by a white cat?

 

Answer 1

So you want to think of these as two following cases.

1st case: A white cat escapes.

2nd case: A black cat escapes given a white cat escaped first.

Probability formula would be as follows:

P(white cat escapes)*P(black cat escapes | white cat escapes)

= [(#white cats)/(# total cats)]*[(#black cats)/(#total cats)]

so 7/13 is the probability a white cat escapes. Then if a second cat escapes, there are 12 remaining if a cat already left. So the probability a black cat escapes after a white cat is 6/12.

So the answer would be (7/13)*(6/12) = (7/26)