If X~B(20, .04)
What is the probability P(X=12)
The probability P(X=12) can be calculated using the probability mass function (PMF) of the binomial distribution.
The PMF formula for a binomial distribution is given by:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- C(n, k) represents the binomial coefficient, which is the number of ways to choose k successes from n trials.
- p is the probability of success in a single trial.
- (1-p) is the probability of failure in a single trial.
- n is the total number of trials.
In this case, X~B(20, .04), which means the number of trials is 20 and the probability of success in a single trial is 0.04.
Using the PMF formula, we can calculate P(X=12) as follows:
P(X=12) = C(20, 12) * 0.04^12 * (1-0.04)^(20-12)
Calculating the binomial coefficient:
C(20, 12) = 20! / (12! * (20-12)!)
= 20! / (12! * 8!)
Calculating the probabilities:
P(X=12) = (20! / (12! * 8!)) * 0.04^12 * (0.96)^8
Note: The factorial function "!" represents the product of all positive integers less than or equal to the given number.
To calculate the final probability, you would need to substitute the values into the formula and perform the calculations.