Final answer:
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.