Ten people, 6 boys and 4 girls are playing on the playground. Miss Tweedle selects a group of 5 at random. What is the probability that the group has 3 boys and 2 girls?

Question

amistre64 · Answer

C(5,3) .6^3 .4^2  maybe?

anonymous · Answer

do i multiply.......?

amistre64 · Answer

.3456 if i did it right :)

amistre64 · Answer

its a binomial distribution; b=.6 and g=.4

bbbbb

bbbbg
bbbgb
bbgbb
bgbbb
gbbbb

bbbgg
bbgbg
bgbbg
gbbbg
bbggb
bgbgb
gbbgb

etc

anonymous · Answer

ohhh so is there any formula for this? like nCr?

amistre64 · Answer

yes

amistre64 · Answer

C(n,r) tends to be a simpler way to express it

anonymous · Answer

soo its 6C3 and 4C2?

amistre64 · Answer

5 pick 3 boys = C(5,3) b^3 g^2

anonymous · Answer

5C3, 5C2, 6C3, 4C2 ?

amistre64 · Answer

not quite .... its a binomial distribution

amistre64 · Answer

6/10 * 5/9* 4/8 * 4/7 * 3/6 is more like it

anonymous · Answer

ohh thankyou, so after i solve all of that, what do i do?

anonymous · Answer

Not quite, that's assuming you pick three boys in row, followed by two girls

amistre64 · Answer

you multiply it by the number of ways there are to pick that

amistre64 · Answer

5C3 ways to do so

anonymous · Answer

4/10 * 3/9 * 6/8 * 5/7 * 4/6, two girls followed by three boys, slightly different probability

anonymous · Answer

so i do 5C3 then 5C2?

amistre64 · Answer

bbbgg
bbgbg
bgbbg
gbbbg

bbggb
bgbgb
gbbgb

bggbb
gbgbb
ggbbb

10 ways

anonymous · Answer

"4/10 * 3/9 * 6/8 * 5/7 * 4/6, two girls followed by three boys, slightly different probability"

-so do i do that and add them?

amistre64 · Answer

so to recap;

the P(b & b & b & g & g) = $\cfrac{6.5.4.4.3}{10.9.8.7.6}$

and there are 10 ways to pick that so $\cfrac{\cancel{10}.\cancel{6}.5.\cancel{4}.\cancel{4}2.\cancel{3}}{\cancel{10}.\cancel{9}3.\cancel{8}\cancel{2}.7.\cancel{6}}$=$\cfrac{10}{21}$

amistre64 · Answer

that is such a pain to type :)

anonymous · Answer

oh im sorry :(

anonymous · Answer

10*9*8*7*6 comes from the 5 group i get that
6,5,4 for boys and 4,3 for girls...

anonymous · Answer

ohh i get it :D thankyou!!!

anonymous · Answer

That makes sense. I wouldn't call it a binomial distribution though, because the probability of picking a boy or girl is not constant (i.e., no independence between trials).

amistre64 · Answer

yay!! :)

amistre64 · Answer

yeah, i saw that it wasnt binomial after i started decresing the boy girl count lol

anonymous · Answer

thankyou so so so so much :) biggest help i've ever gotten today :)

amistre64 · Answer

binomial-ish at best ;)