statistics and probabilities

Question

If a seed is planted, it has a 60% chance of growing into a healthy plant.

If 6 seeds are planted, what is the probability that exactly 3 don't grow?

Answer 1

x = number of seeds that grow is a binomial variable (each seed is independent, two outcomes = grow or don't grow, fixed number of seeds = 6 and fixed probability of 60% to grow).

If probability is 60% that a seed will grow, then it the probability is 40% that a seed will not grow. A successful event here is that the seed does not grow.

x n-x

Binomial Probability = C p (1-p)

n x

where n = number of events (6), x = number of successes (3) and p = probability of success = 0.40

3 3

Binomial Probability = C (0.4) (0.6) = 0.27648

6 3