The probability of a male birth is 0.6. In 2000 families of 4 children each:

The probability of a male birth is 0.6. In 2000 families of 4 children each:

a)How many would you expect to have at least one girl?
b)How many would you expect to have no boys?
c)How many would you expect to have 1 or 2 boys?

a) probability of at least one girl = 1 - probability of all boys
= (1 - 0.6*0.6*0.6*0.6) = 0.8704
number of families = 0.804 * 2000 = 1740.8

b) probability of no boy = probability of all girls
= (0.4*0.4*0.4*0.4) = 0.0256
number of families = 52.1

c) probability of 1 or 2 boys = 1 - probability of no boy - probability of 4 boy - probability of exactly3 boy
=1 - probability of all girls - probability of all boys - probability of exactly 1 girl
= 1 - 0.0256 - 0.6*0.6*0.6*0.6 - (0.4*0.6*0.6*0.6 * 4) = 0.4992
number of families = 2000 * 0.4992 = 998.4

Note: the *4 in probability of 1 girl is because there is 4 ways to achieve 1 girl:
G B B B
B G B B
B B G B
B B B G

a)
No. of expecting least one girl
= (1-0.6^4) * 2000
= 1740.8
= 1741

b)
No. of expecting no boys
= (0.4^4) * 2000
= 51.2
= 51

c)
No. of expecting 1 or 2 boys
= (0.6*0.4*0.4*0.4*4 + 0.6*0.6*0.4*0.4*6) * 2000
= 998.4
= 998

a) One girl and three boys = (0.4)(0.6)^3 =0.0864
Two girls and two boys = (0.4)^2*(0.6)^2 =0.0576
Three girls and one boy = (0.4)^3(0.6)= 0.0384
Four girls and no boy = (0.4)^4 =0.0256
By adding all =0.0864+0.0576+0.0384+0.0256 = 0.208 ..............Ans

b) 0.0256 ............................Ans

c) 0.0384+0.0576 = 0.096 ...............Ans