Answer:
1.875 is the expected number of children the couple will have.
Explanation:
The probability of an event X is denoted by P(X).
Let assume that X is the number of children to whom the couple will give birth. The couple can have at most four children with the following probabilities.
- The couple will have one child if the first is boy, thus:
For one child P(X)=1/2=0.50
- The couple will have two children if the first is girl and the second is a boy, thus:
For two children P(X)=0.5×0.5=0.25
- The couple will have three children if the first two are girls and the third is a boy, thus:
For three children P(X)= 0.5×0.5×0.5=0.125
- The couple will have four children if the first three are girls and the fourth is a boy, or if all the four are girls. thus:
For four children P(X) =(0.5×0.5×0.5×0.5)+(0.5×0.5×0.5×0.5)=0.125
Now calculating the expected number of children the couple will have:
NOTE: Formula is given in the attached pic
Expected number of children = E(X)= (1×0.50)+(2×0.25)+(3×0.125)+(4×0.125)
E(X)= 1.875
