The probability of a seed germinated is 1/3.if three
of the seed are planted what is the probability that only one will germinate
To find the probability that only one seed will germinate out of three, we need to calculate the probability of one seed germinating and the other two not germinating.
The probability of a seed germinating is 1/3, so the probability of a seed not germinating is 1 - 1/3 = 2/3.
To calculate the probability of only one seed germinating, we multiply the probability of one seed germinating (1/3) by the probability of the other two seeds not germinating (2/3 * 2/3):
(1/3) * (2/3 * 2/3) = 2/27
Therefore, the probability that only one seed will germinate out of three is 2/27.
To find the probability that only one seed will germinate out of three planted seeds, we need to use the binomial probability formula:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
Where:
P(X = k) is the probability of getting exactly k successes
n is the total number of trials
k is the number of successful trials
p is the probability of success in a single trial
In this case, n = 3 (total number of planted seeds), k = 1 (number of successful germinations), and p = 1/3 (probability of germination).
Using the formula, the probability that only one seed will germinate is:
P(X = 1) = (3 choose 1) * ((1/3)^1) * ((2/3)^(3-1))
Calculating this:
P(X = 1) = (3! / (1! * (3-1)!)) * (1/3) * (2/3)^2
= (3 * 2 * 1 / (1 * (2 * 1))) * (1/3) * (4/9)
= 3 * 1/3 * 4/9
= 12/27
= 4/9
Therefore, the probability that only one seed will germinate out of three planted seeds is 4/9.
To calculate the probability that only one seed will germinate out of three, we can use the binomial probability formula.
The binomial probability formula is given by:
P(x) = (nCx) * p^x * (1-p)^(n-x)
Where:
P(x) represents the probability of exactly x successes,
nCx represents the number of ways to choose x items from a set of n items (also known as combinations),
p represents the probability of success for each individual trial,
x represents the number of successes, and
n represents the total number of trials.
In this case, the probability of a seed germinating is 1/3. Therefore, p = 1/3.
We want to find the probability that only one seed will germinate out of three, so x = 1.
The total number of trials is three, so n = 3.
Now, let's substitute these values into the formula and calculate the probability:
P(1) = (3C1) * (1/3)^1 * (1 - 1/3)^(3-1)
= 3 * (1/3) * (2/3)^2
= 3 * (1/3) * (4/9)
= 12/27
= 4/9
Therefore, the probability that only one seed will germinate out of three is 4/9.