If a seed is planted, it has a 60% chance of growing into a healthy plant. If 8 seeds are...

Question:

If a seed is planted, it has a 60% chance of growing into a healthy plant.

If 8 seeds are planted, what is the probability that exactly 1 doesn't grow?

Binomial Random Variable

Binomial random variable is known as "binomial" because it is based on two outcomes. When the distribution has more than two outcomes, we use multinomial probabilities.

Answer and Explanation:

Given that number of trials, {eq}n {/eq} = 8 and probability of success, {eq}p {/eq} = 0.40 and probability of failure, {eq}q {/eq} = 1 - 0.40 = 0.60

Since the number of trials are independent and there are two outcomes : plant grow or doesn't grow, we use binomial distribution

{eq}P (X = x) = \binom{n}{x} (p)^x(q)^{n-x} {/eq}

We have to compute that probability of 1 doesn't grow i.e P (X = 1)

{eq}P (X = 1) = \binom{8}{1} (0.4)^1(0.6)^{7} {/eq}

P (X = 1) = 0.0896

Hence, the probability that exactly 1 doesn't grow is 0.0896.

Learn more about this topic:

What is the Binomial Theorem?

from Math 101: College Algebra

Chapter 11 / Lesson 3
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