Probability of seeds

Question

If a seed is planted, it has a 75% chance of growing into a healthy plant.

If 8 seeds are planted, what is the probability that exactly 3 don't grow?

Answer 1

The probability that exactly 3 don't grow is the same as the probability that 5 do grow.

Sample size = 8

each seed is an independent sample

probability of growth 0.75 is constant

seed either grows or doesn't grow

experiment meets requirements of a binomial trial and binomial formula can be used to compute probability

probability of k successes in n trials with probability p of success:

n! k n-k

---- p (1-p)

k!(n-k)!

plug in n = 8, k = 5 and p = 0.75 to determine probability