Question

A small voting district has 101 female voters and 95 male voters .A random sample of 10 voters is drawn .what is probability that exactly 7 of the voters will be female?

Answer 1

To find the probability that exactly 7 of the voters will be female, we need to find in how many ways we can choose 7 female out of 101, multiply it by amount of ways how we choose 3 male out of 95 (we need to complete group of 10 people), and divide this by amount of combinations we can choose a group of 10 people out of 196.

$P(A) = \frac{C(101,7)\cdot C(95,3)}{C(196,10)}=\frac{101!\; 95! \; 186! \;10!}{7!\;94!\;3! \;92! \; 196!} = 0.130$