What is the Probability of Gender Combinations in a Family with Four Children?

[NoPhysicsGenius]

Homework Statement

The probability for a boy to be born is 51.3%.
The probability for a girl to be born is 48.7%.
The probabilities are independent of the sex of any children previously born to a family.
A couple has four children.
(a) What is the probability that all four children are girls?
(b) What is the probability that 3 children are boys and 1 child is a girl?

Homework Equations

The product rule for probability (?)

The Attempt at a Solution

(a) I am thinking that if it were equally likely that a boy or a girl was to be born, then the probability that all four children being girls would be 1/16 = 0.0625 = 6.25%.

However, with the probability of a single girl being born being 48.7%, I am wondering if I could use the product rule to say that the probability that all four children are girls is: 48.7% x 48.7% x 48.7% x 48.7% = 0.0562 = 5.62%. Is this correct?

(b) I am thinking that if it were equally likely that a boy or a girl was to be born, then the probability that all three children being boys and 1 child being a girl would be 4/16 = 1/4 = 0.25 = 25%.

However, with the probability of a single girl being born being 48.7%, I haven't the slightest clue how to proceed with this problem ... Could someone please grant me some assistance?

Thank you.

 

[rock.freak667]

I would do that same thing for the first part but for the 2nd problem I think it would be
P(BBBG)=51.3%x51.3%x51.3%x48.7% x 4!/3!

Note: multiply by 4!/3! because of the order in which the children can be born in

 

[NoPhysicsGenius]

Thanks! I think that does it.