Question

If a seed is planted, it has a 80% chance of growing into a healthy plant. If 7 seeds are planted, what is the probability that exactly 4 don't grow

Answer 1

The probability that exactly 4 don't grow is P=0.0287.

Explanation:

This random variable can be modeled with a binomial distribution.

The sample size is n=7, the total amount of seeds planted.

The probability of success is p=0.8.

The probability that k seeds grow in the sample is:

`P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\\\\\\P(x=k) = \dbinom{7}{k} 0.8^(k) 0.2^(7-k)\\\\\\`

If exactly 4 don't grow, this means that exactly 7-4=3 seeds grow.

Then, we have to calculate P(x=3):

`P(x=3) = \dbinom{7}{3} 0.8^(3)\cdot 0.2^(4)=35*0.512*0.0016=0.0287\\\\\\`