probability distributions aand predicitions

[thelazyman]

Hi, I need help with this following question:


A family hopes to have six children. Assume boys and girls are born with the same probability:

(a) Determine the probability that four of the children will be boys
(b) Determing the probability that 2 of the children will be girls
(c) Determine the probability that 6 of the children will be girls.


Please tell me how to get started on this question.

 

[pka]

A family hopes to have six children. Assume boys and girls are born with the same probability:
(a) Determine the probability that four of the children will be boys
(b) Determing the probability that 2 of the children will be girls
(c) Determine the probability that 6 of the children will be girls.

The point is using equal probabilities, for any string of six the probability is (.5)<SUP>6</SUP>.
P(BBBBGG)= (.5)<SUP>6</SUP>, but that string can appear in (6!)/[(4!)(2!)] ways. So probability of having 4 boys & 2 girls is (.5)<SUP>6</SUP>*{(6!)/[(4!)(2!)]}.