Question

A couple plan s 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. (Assume boys and girls are equally likely.)

a) Create a probability model for the number of children they might have.
b) Find the expected number of children.
c) Find the expected number of boy s they 'll have.

Answer 1

b) 1.75 c) 0.875

Explanation:

lt is 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 possible combination for the number of children that a couple might have :

X 1st girl 1st boy, 2nd girl 1st ,2nd boys,3rd girl 1,2,3rd boys Probability- 0.5 0.25 0.125 0.125

b) Expected number of children :

1(0.5) + 2 ( 0.25 ) + 3 ( 0.125) + 3( 0.125)

= 1+ 0.75

= 1.75

c) Expected number of boys :

0 x 0.5 + 1 x 0.25 + 2 x 0.125 + 3 x 0.125

= 0.875