# 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)

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)

Expert's answer

(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

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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