Question

in a family with 4 children excluding multiple births what is the probability of having four girls? Assume that a girl is as likely as a boy.

Answer 1

50%

Answer 2

how did you determine that? I am still learning all of this and am overthinking it all.

Answer 3

Look at all possibilities for boys and girls xxxx, where each x can be a boy or a girl. We will have something like

gggg
gggb
ggbg
ggbb
gbgg
gbgb
gbbg
gbbb
bggg
bggb
bgbg
bgbb
bbgg
bbgb
bbbg
bbbb

Now some may appear redundant, but they are not because for example, ggbb means the oldest child is a girl and the youngest is a boy, while for bbgg means that the oldest is a boy and the youngest is a girl. So they are different.

So the probability of all girls is just 1/16, since in only one case is there a family with all girls.

Answer 4

That makes good sense. So in essence because there are 2 options for each child 1/2 * however many children?

Answer 5

yes!!

Answer 6

Actually, (1/2)^(number of children), which is what I thought you meant.

Answer 7

You got it - thanks so much!

Answer 8

yw