SOLUTION: Assume that, when a child is born, the probability it is a girl is ½ and that the sex of the child does not depend on the sex of an older sibling. Find the probability distributi

Question 1198349: Assume that, when a child is born, the probability it is a girl is ½ and that the sex of the child does not depend on the sex of an older sibling. Find the probability distribution for the number of girls in a family with 4 children

Found 2 solutions by ewatrrr, math_tutor2020:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
the probability it is a girl is ½
Find the probability distribution for the number of girls in a family with 4 children
(1/2)(1/2)(1/2)(1/2) = 1/16
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

It appears that the tutor @ewatrrr might have misread the question.

The task is to find the probability distribution for the number of girls in this family. The teacher wants a probability table showing all the possible outcomes, and associated probabilities.

Convention is to use the binomial distribution. However, I'll take a different approach.

X = number of girls
X ranges from X = 0 to X = 4

The calculation @ewatrrr has provided applies to both X = 0 girls (aka 4 boys) and also X = 4 girls (0 boys) due to symmetry.

B = boy
G = girl

X = 0 girls
BBBB

X = 1 girl
BBBG
BBGB
BGBB
GBBB
There are four cases where the family has 1 girl
We can see this using the nCr formula with n = 4 and r = 1.

X = 2 girls
BBGG
BGGB
BGBG
GBBG
GBGB
GGBB
There are six cases where the family has 2 girls
This value (6) can be calculated by computing the nCr value when n = 4 and r = 2.

X = 3 girls
GGGB
GGBG
GBGG
BGGG
There are four cases where the family has 3 girls (notice the similar structure to the X = 1 girl case)
This value (4) can be calculated by computing the nCr value when n = 4 and r = 3.

X = 4 girls
GGGG
There is one case where the family has 3 girls (notice the similar structure to the X = 0 girls case)
There's no need to use nCr here, but if you wanted then it would be n = 4 and r = 4.

There are 2^4 = 16 ways to have four kids.

This is the probability distribution

X P(X)
0 1/16
1 4/16
2 6/16
3 4/16
4 1/16

Thing to notice: The numerators 1,4,6,4,1 are found in the same row of Pascal's Triangle
I decided to not reduce the fractions to keep the denominators consistent.

This is what it looks like after reducing those fractions

X P(X)
0 1/16
1 1/4
2 3/8
3 1/4
4 1/16

Another thing to notice: The P(X) values add to 1.

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