Acouple plans to have children until they get a boy, but they agree that they will not have more than four children even if all are girls. find the expected number of children they will have. assume that boys and girls are equally likely. (round your answer to three decimal places.)

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.

For one child P(X)=1/2=0.50

For two children P(X)=0.5×0.5=0.25

For three children P(X)= 0.5×0.5×0.5=0.125

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

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