What is the probability that at least one mouse is female, given that exactly one is gray?

Question

Assume that you have 10 mice in the cage: 4 white males, 3 gray females, and 3 gray males. Two mice are selected simultaneously and at random, and their colors are noted.
What is the probability that at least one mouse is female, given that exactly one is gray?

Answer 1

Dear Kate,

 

Assume that you have 10 mice in the cage: 4 white males, 3 gray females, and 3 gray males. Two mice are selected simultaneously and at random, and their colors are noted.
What is the probability that at least one mouse is female, given that exactly one is gray?

 

Conditional probability tells us:

P(B|A) = [P(A intersect B)] / P(A)

or in English, the probability of the second condition, given that the first condition is the probability of both conditions being true divided by the probability of the first condition being true.

 

In this case, the probability that your selection of two mice has exactly one female mouse, given that exactly one mouse is gray.

What's the probability that exactly one mouse of the two is gray? = P(A)

What is the possibility that one or two of those chosen gray mouses are female? P(A intersect B)

Plug and chug into the above question and voila! 

 

If you would like an online tutor, I am available!

Me'ira