# Thread: Married couple raffle question.

1. ## 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) $n(s) = 8C2 = 120$
$n(married couples) = 8$
So, that means that it's 8/120, or 1/15.

b) $(\frac {8}{16})(\frac {7}{15})$
$= \frac {7}{30}$

c) $n(s) = 16C6 = 8008$
There are 8 married couples, so 8C3.
$\frac {56}{8008}$
$\frac {1}{143}$

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.

2. 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:

$n(s) \:=\: _8C_2 \:=\: 120$

$n(\text{married couples}) \:=\: 8$

So, that means that it's: . $\frac{8}{120} \:=\:\frac{1}{15}$ . . 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: . $\frac{16}{16} \:=\:1$

The second must be one of the other 7 people of the same sex: . $\frac{7}{15}$

Therefore: . $P(\text{same sex}) \;=\;\frac{7}{15}$

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

Another approach . . .

There are 120 possible outcomes.

$\text{We want: }\:\begin{Bmatrix} \text{2 men:} & _8C_2 \:=\:28\text{ ways} \\

\text{or} \\ \text{2 women: } & _8C_2\:=\:28\text{ ways} \end{Bmatrix}$

Therefore: . $P(\text{same sex}) \;=\;\frac{56}{120} \;=\;\frac{7}{15}$

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

$n(s) \:=\:_{16}C_6 \:=\:8008$

There are 8 married couples, so: . $_8C_3 \:=\:56$

Therefore: . $\frac{56}{8008} \:=\:\frac{1}{143}$ . . Yes!