4. (20 points) Assume that boys and girls are equally likely to be born (a) (2 p

Question

4. (20 points) Assume that boys and girls are equally likely to be born (a) (2 points) If a couple gave birth to three babies, what is the sample space? (Use b for boys and g for girls) (b) (5 points) Write down the corresponding simple events associated with the following events: A = {all boys), B = {all girls), C-{exactly one girl], D-(exactly one boy), and E- (at least one boyJ Math 150 Mierm 2- Page 6 of S November, 2017 (c) (5 points) Caleulate P(A), P(B), P(C), P(D), P(E). (d) (2 points) What does P(A) P(B) + P(C) + P(D) equal? What does this tell you?

Explanation / Answer

a) if a couple gave birth to three babies.

b:boy and g : girl

The sample space is

S = { bbb,bbg,bgb,bgg,ggb,gbg,gbb,ggg} ,

n(S)=no. of elements in the sample space= 8

b) A: All boys

A={ bbb}

B: All Girls

B={ggg}

C: Exactly one girl

C={ bbg, bgb,gbb}

D: Exactly one boy

D={ bgg,gbg,ggb}

E: Atleast one boy

E={ bbb,bbg, bgb,bgg,gbb,gbg,ggb}

C) P(A) = n(A)/n(S) = 1/8

P(B) = n(B)/n(S) = 1/8

P(C) = n(C)/n(S) = 3/8

P(D) = n(D)/n(S) = 3/8

P(E)= n(E)/n(S) = 7/8

d) P(A)+P(B)+P(C)+P(D)=1/8+1/8+3/8+3/8 = 1

The events A,B,C,D forms a sample space. i.e. The union of events A, B, C, D is sample space

AUBUCUD= { bbb,bbg,bgg,bgb,gbb,gbg,ggb,ggg}=S

The probabiblity of sample space is one.

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