Question

If a seed is planted, it has a 85 % chance of growing into a healthy plant. If 7 seeds are planted, what is the probability that exactly 1 doesn't grow?

Answer 1

To find the probability that exactly 1 seed doesn't grow out of 7 planted seeds, we can use the binomial probability formula. Plugging in the values, we get a probability of approximately 0.000012625945.

Step-by-step explanation:

To find the probability that exactly 1 seed doesn't grow out of 7 planted seeds, we need to use the binomial probability formula.

The formula is:

P(X=k) = C(n,k) imes p^k imes (1-p)^(n-k)

Where:

P(X=k) is the probability of getting exactly k successes,

C(n,k) is the number of combinations of n items taken k at a time,

p is the probability of success,

n is the number of trials

k is the number of successful trials.

In this case, n = 7 (number of seeds planted), p = 0.85 (probability of seed growing), and k = 1 (exactly 1 seed doesn't grow).

Plugging in the values into the formula:

P(X=1) = C(7,1) imes 0.85^1 imes (1-0.85)^(7-1)

P(X=1) = 7 imes 0.85 imes 0.15^6

P(X=1) = 7 imes 0.85 imes 0.000002076299

P(X=1) ≈ 0.000012625945

Therefore, the probability that exactly 1 seed doesn't grow out of 7 planted seeds is approximately 0.000012625945.