In a binomial experiment with and . Find
0.9972
0.0366
0.0228
0.0866
To find the probability of a binomial experiment with n trials and a success rate of p, we use the formula:
P(X = x) = (nCx) * p^x * (1-p)^(n-x)
Where:
- n is the number of trials
- x is the number of successful outcomes
- p is the probability of success on a single trial
- (nCx) is the number of ways to choose x successes out of n trials
Given n = 4 and p = 0.2, we need to find:
P(X = 0), P(X = 1), P(X = 2), P(X = 3), P(X = 4)
1. P(X = 0):
P(X = 0) = (4C0) * (0.2)^0 * (0.8)^4 = 1 * 1 * 0.4096 = 0.4096
2. P(X = 1):
P(X = 1) = (4C1) * (0.2)^1 * (0.8)^3 = 4 * 0.2 * 0.512 = 0.4096
3. P(X = 2):
P(X = 2) = (4C2) * (0.2)^2 * (0.8)^2 = 6 * 0.04 * 0.16 = 0.0384
4. P(X = 3):
P(X = 3) = (4C3) * (0.2)^3 * (0.8)^1 = 4 * 0.008 * 0.8 = 0.0256
5. P(X = 4):
P(X = 4) = (4C4) * (0.2)^4 * (0.8)^0 = 1 * 0.0016 * 1 = 0.0016
So, the probabilities are:
P(X=0) = 0.4096
P(X=1) = 0.4096
P(X=2) = 0.0384
P(X=3) = 0.0256
P(X=4) = 0.0016
Therefore, the answer is not in the provided options.