Probability Q

Dec 2009
61
0
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.
 
Dec 2009
3,120
1,342
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

\(\displaystyle \frac{\binom{9}{3}+\binom{9}{2}\binom{3}{1}}{\binom{12}{3}}\)
 
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