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

Question

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)

Answer 1

(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