Ten peas are generated from parents having the green/yellow pair of genes, so that there is a 0.45 probability that an individual pea will have a green pod. Find the probability that are least 1 offspring had a green pod among the 10 offspring peas.

#### Solution

Let $p$ be the probability that an individual pea have a green pod.

Given that `$p=0.45$`

.

`$n=10$`

peas are generated from parents having the green/yellow pair of genes.

The random variable $X$ is number of offspring have a green pod among the 10 offspring peas.

Here `$X\sim B(10, 0.45)$`

.

The probability mass function of $X$ is

` $$ \begin{aligned} P(X=x) &= \binom{10}{x} (0.45)^x (1-0.45)^{10-x},\\ &\quad x=0,1,\cdots, 10. \end{aligned} $$ `

The probability that at least one offspring had a green pod among the 10 offspring is

` $$ \begin{aligned} P(X\geq 1) &= 1- P(X\leq 0)\\ & = 1- \binom{10}{0}(0.45)^0(1-0.45)^{10}\\ & = 0.0025 \end{aligned} $$ `

#### Further Reading

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