Expert: Jack Cheng - 2/19/2007

Question
There are 9 married couples attending a party where two door prizes (the prizes are the same) are awarded to two different people. Solve to 3 decimal places.
What is the probability a married couple wins the prizes?
What is the probability one prize goes to a man and one to a woman?
If John's wife Mary wins a prize, what is the probability that John will also win a prize?
If Mary does not win a prize, then what is the probability that John will?  

Answer
Hi Susan

What is the probability a married couple wins the prizes?

I think it's 1/17. The first win can be any person, but the second win has to be that persons' spouse, a chance of 1 out of 17 people (assuming spouse can't play again).

What is the probability one prize goes to a man and one to a woman?

(1/2)(9/17) = 9/24; first time, half of the people; second time, 9 male/female out of 17 people.

If John's wife Mary wins a prize, what is the probability that John will also win a prize?

1/17; one person out of 17 possibilities.

If Mary does not win a prize, then what is the probability that John will?

2/17; two chances out of 17 people

I hope this helps,
Jack