Answer to Question #6854 in Statistics and Probability for Jason Tanger

Question #6854
A family has three children. Using b to stand for boy and g for girl give the following. (To indicate that the first child is a boy, the second child is a boy, and the third child is a girl enter bbg. Enter your answers as a comma-separated list.) (a) the sample space S = (b) the event E that the family has exactly two daughters E = (c) the event F that the family has at least two daughters F = (d) the event G that the family has three daughters G = Give the following. (Assume that boys and girls are equally likely. Enter your probabilities as fractions.) (e) p(E) (f) p(F) (g) p(G) (h) o(E) (i) o(F) (j) o(G)
1
Expert's answer
2012-02-24T09:48:32-0500
(a) the sample space
S = {ggg,ggb,gbb,bbb } &
Here ggb=gbg=bgg& 'cause it does not matter in which order we count boys &girls

(b) the event E that the family has exactly two daughters
E = {ggb }

(c) the event F that the family has at least two daughters
F ={ ggb,ggg }
(d) the event G that the family has three daughters
G = {ggg}
Give the following. (Assume that boys and girls are equally likely. Enter your probabilities as fractions.)
(e) p(E)=|E|/|S|=1/4=0.25
(f) p(F)=2/4=0.5
(g) p(G)=1/4=0.25

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