probablity problem about children and girls

[abja537363]

A family has 3 natural children and has adopted 2 girls. Each natural child has equal probability of being a girl or a boy, independent of the other children. Let random variable X be the number of girls. Describe probability space (Sl,A, P), define random variable X, find PMF, expectation and variance of X.

 

[Steven G]

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What does SI, A and P mean??

What values can X take on? What is the probability for each value of X?

 

[HallsofIvy]

With three children, each equally likely to be a girl or a boy there are 2^3= 8 equally likely families:
GGG
GGB
GBG
GBB
BGG
BGB
BBG
BBB

With two additional girls, those become
GGGGG
GGBGG
GBGGG
GBBGG
BGGGG
BGBGG
BBGGG
BBBGG

The minimum number of girl is, of course, 2 and there is exactly one case of that, BBBGG.
P(2)= 1/8.
There are three cases with 3 girls, GBBGG, BGBGG, and BBGGG.
P(3)= 3/8.
There are three cases with 4 girls, GGBGG, GBGGG, and BGGGG,
P(4)= 3/8.
There is one case with 5 girls, GGGGG,
P(5)=1/8.

Those all add to 1 of course.