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%

 97.7%

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