Combination - Probability. Probability within a set of 2 I am stuck on a homework question. The question is

If there are 6 couples. (12 individuals) and 6 prizes are to be given out to these 12 individuals. What is the probability of a couple receiving a price.

I know that there are $^{12}C_6$ possible ways to give out a prize. So that is the total number of outcomes.

Whats confusing me is how should I find the probability of the set consisting of 2 people i.e a couple
any hints to help me out?

Edit any one can receiv a price, Even two people who are coupled

Assuming you are looking at a particular couple and you want the probability that at least one wins a prize, you could approach it by considering:


*

*What is the probability the first member of the couple wins a prize?

*If the first member of the couple does not win a prize, what is the conditional probability the second wins a prize? Multiply this by the probability the first member of the couple does not win a prize.

*Add the two previous results together 


Another approach giving the same result:


*

*What is the probability the first member of the couple does not win a prize? 

*If the first member of the couple does not win a prize, what is the conditional probability the second does not win a prize?

*Multiply these together to get the probability the couple does not win a prize.

*Find the probability the couple wins at least one prize

