• Dec 18th 2009, 05:34 AM
dominion
I am trying to help my cousin and I am unable to get the answer that is given by the book:

Question is:

A survey is carried out on a group of 100 students, 60 of whom are boys.

Find the probability that any 2 students chosen at random from the original group will be both girls.

thanks
• Dec 18th 2009, 08:13 AM
Soroban
Hello, dominion!

Quote:

A survey is carried out on a group of 100 students, 60 of whom are boys.

Find the probability that any 2 students chosen at random from the original group will be both girls.

I assume that the choosing is done without replacement.

There are: 60 boys and 40 girls.

Method #1

There are: . ${100\choose2} \:=\:4950$ possible pairs of students.

To choose 2 girls, there are: . ${40\choose2} \:=\:780$ ways.

Therefore: . $P(\text{noth girls}) \;=\;\frac{780}{4950} \;=\;\frac{26}{165}$

Method #2

The probability that the first student is a girl is: . $\frac{40}{100}$
The probability that the second student is a girl is: . $\frac{39}{99}$

Therefore: . $P(\text{both girls}) \;=\;\frac{40}{100}\cdot\frac{39}{99} \;=\;\frac{26}{165}$