A cage holds 6 black cats and 9 white cats, if two cats escape what is the probability of both cats being white?

Question

A cage holds 6 black cats and 9 white cats, if two cats escape what is the probability of both cats being white?

Answer 1

This involves two events, each with their own probability. Because both the first AND the second have to happen for this problem, you will MULTIPLY the wo individual probabilities.

Total cats = 15, White cats = 9

Probability first escaped cat is white = 9/15

One white cat has now escaped, so we now have Total cats = 14, White cats = 8

Probability second escaped cat is white = 8/14

Now MULTIPLY because this is an AND probability problem. (9/15)(8/14) = 72/210 = 12/35

Answer 2

Hello, thank you for taking the time to post your question!

There will be two separate draws on this one … the first one has 15 choices, 9 of which are white. And then the second one has 14 choices, 8 of which are white (because you can assume that the one that was removed was white for this scenario to work).

That means you can find the combined probability by taking

9/15 x 8/14 = 72/210 = 12/35 = 0.3429

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)