Hi, I'm a bit confused with one part of this probability problem. I'm pretty sure I got part a and b, but I'm not sure about c.
A family has 5 children, determine the following probabilities
a.) All 5 are the same gender
b.) 3 are boys, and 2 are girls
c.) The 3 oldest are boys, and the 2 youngest are girls.
For a. I'm pretty sure it's 1/32 since it would be .5^5 b/c there's a 1/2 probability of being either gender for each of the 5 children.
For b. I think it's also 1/32 since the probability of either gender doesn't change per birth.
As far as c. is concerned I think it's 5/16 because C(5,3) = 10 ways to have 3 boys and 2 girls multiplied by 1/32 but I'm not sure