Answer:
The probability that exactly 4 don't grow is P=0.0287.
Step-by-step 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:
[tex]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}\\\\\\[/tex]
If exactly 4 don't grow, this means that exactly 7-4=3 seeds grow.
Then, we have to calculate P(x=3):
[tex]P(x=3) = \dbinom{7}{3} 0.8^{3}\cdot 0.2^{4}=35*0.512*0.0016=0.0287\\\\\\[/tex]
