Thread: Probability Q

Hi I need help with this question
3 chidlren are chosen at random from 9 girls and 3 boys. What is the probability that
i. at least one boy is chosen?
ii. more girls than boys are chosen?

I've got that the possible outcomes is 55 but I dont know what to do next.
Thanks.

Originally Posted by Detanon

Hi I need help with this question
3 chidlren are chosen at random from 9 girls and 3 boys. What is the probability that
i. at least one boy is chosen?
ii. more girls than boys are chosen?

I've got that the possible outcomes is 55 but I dont know what to do next.
Thanks.

(i)

At least 1 boy means "more than no boys"

$\displaystyle P(no\ boys)=\frac{\binom{9}{3}}{\binom{12}{3}}$

which is the probability all 3 are girls.
Select 3 girls from 9, divide by the selections of 3 children from 12.

then subtract this from 1.

(ii)

more girls than boys means 3 girls or 2 girls with 1 boy

$\displaystyle \frac{\binom{9}{3}+\binom{9}{2}\binom{3}{1}}{\bino m{12}{3}}$