Question

what is the expected number of female children in a family with three children?
1
1.5
2
2.5

Explanation:

Step1: Define probability of a child being female

The probability $p$ of a child being female is $p = 0.5$ since there are two equally - likely genders (male and female). The number of children $n=3$.

Step2: Use the formula for expected value of a binomial distribution

The formula for the expected value $E(X)$ of a binomial random variable $X$ with parameters $n$ (number of trials) and $p$ (probability of success in a single trial) is $E(X)=np$. Here, the "success" is having a female child. Substitute $n = 3$ and $p=0.5$ into the formula: $E(X)=3\times0.5$.

Step3: Calculate the result

$3\times0.5 = 1.5$.

Answer:

1.5