# Solved (Free): Ten peas are generated from parents having the green/yellow pair of genes, so that there is a 0.45 probability

#### ByDr. Raju Chaudhari

Mar 30, 2021

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}