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Probability Problem

Elfen
almost 9 years

Say that a couple has a (11/23)^k probability of having exactly k children, k > 0.

a) Find the probability that a couple does 0 children.

b) Find the probability of a couple having exactly 2 daughters. (a children will become a girl with a probability of 50%)

Elfen
almost 9 years

mandevian says

OH yeah I think I got it. Summation will start with k=2. Therefore 121/552


It's not made out of the same summation, actually finding the formula is much easier than calculating the final result, which needs series theory to be calculated.

Finding the final summation formula is enough.
mandevian
almost 9 years
OH yeah I think I got it. Summation will start with k=2. Therefore 121/552
Elfen
almost 9 years

mandevian says

Have not thought it through but I think it is half of 11 by 12


it's much lower
illuminati
almost 9 yearsedited
Probability Problem:

Chances of OP ever having intercourse and consequently children
mandevian
almost 9 years
Have not thought it through but I think it is half of 11 by 12
mandevian
almost 9 years
I will try to solve the othet one. Still have not figured out the approach.
Elfen
almost 9 yearsedited
When I posted it I had found only A, I found B afterwards, so I'm leaving it here for whoever wants to solve it, so it was indeed a help post, and thank you
mandevian
almost 9 years
Fam I thought you needed help. If you already know the answer to other one as well then I won't spend time on it.
Elfen
almost 9 years
that's correct about zero children @mandevian
mandevian
almost 9 years
For zero children

P (0)= 1-p (1)+p (2)......+p (infinity)

So let 11/23 =a

P (0)= 1- summation for n = 1 to infinity a^n

= 1- (-a/(a-1))

= 1-(-11/23/(-12/23))

=1-(11/12)

=1/12