Don't know where to start...

vedmachka · #1 $Old$ 11-18-2008, 09:20 AM

This problem seemed so simple in the beginning, but now, I am completely confused. I don't even know where to start. Is it just me?

4. In a class of 25 students, there are 13 boys and 12 girls. A committee of 3 students is needed and is to be chosen randomly from the group of 25.

a. What is the probability of the group will have 2 boys and 1 girl?

b. What is the probability of the group having all boys or all girls?

Jhevon · #2 $Old$ 11-18-2008, 09:25 AM

Quote:

Originally Posted by vedmachka $View Post$

This problem seemed so simple in the beginning, but now, I am completely confused. I don't even know where to start. Is it just me?

4. In a class of 25 students, there are 13 boys and 12 girls. A committee of 3 students is needed and is to be chosen randomly from the group of 25.
a. What is the probability of the group will have 2 boys and 1 girl?

this is

$\frac {\text{the total number of (distinct) groups you can form with 2 boys and 1 girl}}{\text{total number of groups of size three}}$

hint: think "combinations"

Quote:

b. What is the probability of the group having all boys or all girls?[/font][/left]

this is $P(\text{all boys}) + P(\text{all girls})$

where $P(\text{all boys}) = \frac {\text{total number of (distinct) groups with 3 boys and no girls}}{\text{total number of groups of size 3}}$

and

$P(\text{all girls}) = \frac {\text{total number of (distinct) groups with 3 girls and no boys}}{\text{total number of groups of size 3}}$

hint: the same as in the last problem