If a seed is planted, it has a 75% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 1 doesn't grow?

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DylaneyH692328 DylaneyH692328 · Answer 1 · 2022-10-31T05:00:11+01:00

Explanation

From the question, we can see that

Probability of sucess = 0.75

Probability of failure = 1-0.75=0.25

n=8

Therefore, we will use the binomial probability distribution formula to find the probability that exactly 1 doesn't grow

[tex]P_x=(nCx)p^xq^{n-x}[/tex]

For exactly one not growing we must have seven success and one failure.

[tex]\begin{gathered} P_7=8C7(0.75)^7(0.25)^1 \\ =\frac{8!}{7!1!}(0.75)^70.25 \\ =8(0.75)^7(0.25) \\ =0.2670 \end{gathered}[/tex]

Answer: 0.2670