Question

A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys.
a) Create a probability model for the number of children that they will have

b) Find the expected number of children

c) Find the expected number of boys that they will have

Answer 1

Answer:

1.75,0.625

Step-by-step explanation:

Given that a couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys.

a) The couples can have

X     I girl         I boy, II  girl             I,II boys, III girl         I,II,III boys

Pr.    0.5               0.25                           0.125                  0.125

b) Expected no of children

=$1(0.5)+2(0.25)+3(0.125)+3(0.125)\\=1+0.75\\=1.750$

c)Expected number of boys

= $0*0.5+1*0.25+2*0.125+3*0.125\\=0.625$