Suppose that the probability of parents having a child with blond hair is 1/4. If there are 6 children in the family, what is the probability that half of them will have blond hair?

#### Solution

Let $X$ denote the number of children with blond hair. Given that `$n=6$`

, `$p=1/4$`

. `$X\sim B(6, 1/4)$`

.

The probability mass function of $X$ is

` $$ \begin{aligned} P(X=x) &= \binom{6}{x} (0.25)^x (1-0.25)^{6-x},\\ &\quad x=0,1,\cdots, 6 \end{aligned} $$ `

The probability that half of them will have blond hair is

` $$ \begin{aligned} P(X=3) &= \binom{6}{3} (0.25)^{3} (1-0.25)^{6-3}\\ &= 0.1318 \end{aligned} $$ `

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators