If a seed is planted, it has a 80% chance of growing into a healthy plant.
If 10 seeds are planted, what is the probability that exactly 2 don't grow?
To calculate the probability that exactly 2 seeds don't grow, we need to use the concept of binomial probability. The binomial probability formula is:
P(x) = (nCx) * p^x * q^(n-x)
Where:
- P(x) represents the probability of getting exactly x successes
- n is the total number of trials (number of seeds planted)
- x is the number of desired successes (number of seeds that don't grow)
- p is the probability of success (probability of a seed growing)
- q is the probability of failure (1 - p)
In this case, we have 10 seeds planted, and the probability of a seed growing is 80%, or 0.8. Therefore, the probability of a seed not growing (failure) is 1 - 0.8 = 0.2.
Let's substitute these values into the formula:
P(2) = (10C2) * (0.8^2) * (0.2^(10-2))
First, let's calculate (10C2) which represents the number of combinations of choosing 2 out of 10 seeds:
(10C2) = 10! / (2! * (10-2)!)
= 10! / (2! * 8!)
= (10 * 9) / (2 * 1)
= 45
Now, let's calculate the probability:
P(2) = 45 * (0.8^2) * (0.2^8)
= 45 * 0.64 * 0.0000016
= 45 * 0.00018432
= 0.00829
Therefore, the probability that exactly 2 seeds don't grow is approximately 0.00829, or 0.829%.