Thread: Married couple raffle question.

Hey, I don't think I am doing this question correctly, my solutions just seem to simple.

Question:
There are 8 opposite-sex married couples at a party. Two people are chosen at random to win a door prize.
a) What is the probability that the 2 people will be married to each other?
b) What is the probability that the 2 people will be of the same sex?
c) If 6 people are chosen, what is the probability that they are 3 married couples?

Solution:
a)

So, that means that it's 8/120, or 1/15.

b)


c)
There are 8 married couples, so 8C3.




I am unsure if any of these are correct, as I am not used to doing these sorts of problems with things like married couples.

Hello, Kakariki!

The problems are simple, but require some careful thinking.
And you did fine!

There are 8 opposite-sex married couples at a party.
Two people are chosen at random to win a door prize.

a) What is the probability that the 2 people will be married to each other?

Solution:





So, that means that it's: . . . Right!

b) What is the probability that the 2 people will be of the same sex?

The first person can be any of the 16 people: .

The second must be one of the other 7 people of the same sex: .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Another approach . . .

There are 120 possible outcomes.




Therefore: .

c) If 6 people are chosen, what is the probability that they are 3 married couples?



There are 8 married couples, so: .

Therefore: . . . Yes!