Question

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

If 7 seeds are planted, what is the probability that exactly 3 don't grow?

Answer 1

Answer:

P(X = 3) = 0.2958 Or 29.58%.

Explanation:

This is a binomial probability problem, where:

n = 7 (number of trials or seeds planted)
p = 0.6 (probability of success or a seed growing)
q = 1 - p = 0.4 (probability of failure or a seed not growing)
We want to find the probability that exactly 3 seeds don't grow, which means we want to find P(X = 3), where X is the number of failures (seeds that don't grow).

Using the binomial probability formula, we have:

P(X = 3) = (7 choose 3) * (0.4)^3 * (0.6)^4

where (7 choose 3) = 35 is the number of ways to choose 3 out of 7 seeds.

Plugging in the values, we get:

P(X = 3) = 35 * 0.064 * 0.1296

P(X = 3) = 0.2958

Therefore, the probability that exactly 3 out of 7 seeds don't grow is 0.2958 or about 29.58%.