Question

Find the probability that in a family of 4 children there will be

a) At least 1 girl

b) At least 1 boy and at least 1 girl

c) Out of 1500 families with 3 children each how many would you expect to have 1 or 2 girls.

Assume that the probability of a female birth is 1/2.

Answer 1

Family of 4 children : Possibilities :

zero boys: 1/16;

one boy: 1/4

two boys: 3/8

three boys: 1/4

four boys: 1/16

Note: 1/16 + 1/4 + 3/8 + 1/4 + 1/16 = 1

a) Family of 4 children : Possibilities:  

Prob(atleast 1 girl) = Prob(1 girl) + Prob(2 girls) + Prob(3 girls) + Prob(4 girls)

Prob(atleast 1 girl) = 1 - Prob(0 girls)

0 girls = 1 possibility (BBBB) out of 16 possibilities

Prob(atleast 1 girl) = 1 - 1/16 = 15/16

b) Prob(atleast 1 B and 1 G) = 1 - (BBBB, GGGG) = 1 - 2/16 = 14/16

c) 3 children - BBB, BBG, BGB, GBB, GGB, GBG, BGG, GGG

Prob ( 1 or 2 girls) = BBG, BGB, GBB, GGB, GBG, BGG = 6/8 = 3/4

Therefore, for 1500 families, 3/4 x 1500 = 1125 famillies