If a seed is planted, it has a 72% chance of growing into a healthy plant. If 5 seeds are planted, what is the probability that exactly 1 grows into a healthy plant?

Question

If a seed is planted, it has a 72% chance of growing into a healthy plant.

If 5 seeds are planted, what is the probability that exactly 1 grows into a healthy plant?

Answer 1

n = 5 seeds

p = 0.72 (seeds to grow healthy)

x = 1 seed selected that will grow healthy

Use X~Bin(5, 0.72).

P(X = 1) = [5! / (1!)(4!)]*(0.72)(0.28)⁴ = 0.02213