If a seed is planted, it has a 90% chance of growing into a healthy plant. if 7 seeds are planted, what is the probability that exactly 4 don't grow?

Given:

p = 90% = 0.9, the probability that the seed grows into a healthy plant.

Therefore

q = 1 - p = 0.1, the probability that the seed will not grow into a healthy plant.

n = 7, the number of seeds planted.

Let r = 4, expected number of seeds that will grow.

Use the Binomial distribution to determine

P (4 of 7 seeds will grow) = ₇C₄ p⁴q ⁽⁷⁻⁴)

= 35 * (0.9⁴) * (0.1³)

= 0.023

P (4 of 7 seeds will not grow) = 1 - P (4 of 7 seeds will grow)

= 1 - 0.023

= 0.977 or 97.7%

Answer: 97.7%