Question

76. Rhubarb Suppose you purchase a bundle of $10$bare-root rhubarb plants. The sales clerk tells you that on average you can expect $5\%$of the plants to die before producing any rhubarb. Assume that the bundle is a random sample of plants. Let $Y=$ the number of plants that die before producing any rhubarb. Use the binomial probability formula to find
$P(Y=1).$ Interpret this result in context.

Short answer

The chance of getting $1$out of $10$plants that die before producing any rhubarb is $31.51\%$.

Step-by-step solution

Given information

An average of $5\%$of the plants to die before producing any rhubarb. Let $Y=$the number of plants that die before producing any rhubarb. And to find the value of $P(Y=1)$.

Explanation

Given:$$\begin{gathered} n=10 \\ p=0.05 \end{gathered}$$

The Binomial Probability:

$$\begin{gathered} \mathrm{P}(\mathrm{X}=\mathrm{k})=\left(\begin{array}{c}n\\ k\end{array}\right)\times p^k\times (1-p{)}^{n-k} \\ \mathrm{P}(1)=\left(\begin{array}{c}10\\ 1\end{array}\right)\times (0.05{)}^1\times (0.95{)}^{10-1} \\ \approx 0.3151 \end{gathered}$$