Answer and solution for this please. Thank you! A class has 8 boys and 15 girls. If three students are selected at a random from the class, what is the probability that they are all boys?

Answer 1

Hi Nyx L.,

Don't guess, don't furiously estimate.

Do figure it as: 1st pick P(boy)=(8/23) (there were 8 boys in a draw from 23)

If it was a boy, then 2nd pick P(boy) = (7/22) (there were only 7 boys left in a draw from 22)

If both the first 2 were boys, 3rd pick P(boy) = (6/21) (there were only 6 boys left in a draw from 21)

So put those all together, P(boys1,2,3) = (8*7*6)/(23*22*21) ~ 0.0316

Frankly, if I were one of the remaining boys, I'd be looking over my shoulder, as the saying goes. The girls aren't going to just assume the picks were random. Just sayin'.

-- Cheers, --Mr. d.