If a seed is planted, it has a 75% chance of growing into a healthy plant.
If 7 seeds are planted, what is the probability that exactly 3 don't grow?
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f a seed is planted, it has a 75% chance of growing into a healthy plant.
If 9 seeds are planted, what is the probability that exactly 2 don't grow?
To find the probability that exactly 3 out of 7 seeds don't grow, we need to use the binomial probability formula.
The binomial probability formula is given by:
P(x) = C(n, x) * p^x * q^(n-x)
Where:
P(x) is the probability of exactly x successes (in this case, the number of seeds that don't grow)
n is the total number of trials (in this case, the total number of seeds planted)
C(n, x) is the number of combinations of n items taken x at a time
p is the probability of success on a single trial (in this case, the probability of a seed not growing)
q is the probability of failure on a single trial (in this case, the probability of a seed growing)
In this case, since a seed has a 75% chance of growing, the probability of success (p) is 0.75. And the probability of failure (q) is 1 - 0.75 = 0.25.
Let's calculate the probability using these values:
P(x = 3) = C(7, 3) * 0.25^3 * 0.75^(7-3)
To calculate C(7, 3), we can use the formula for combinations:
C(n, x) = n! / (x! * (n-x)!)
So,
C(7, 3) = 7! / (3! * (7-3)!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35
Now we can substitute these values back into the original formula:
P(x = 3) = 35 * 0.25^3 * 0.75^4
Calculating this expression gives us the probability that exactly 3 out of 7 seeds don't grow.
rubbish
There's a 25% chance of not growing. So,
P(3 not) = 7C3 .25^3 .75^4 = 0.17