n=13 p=0.75
p (more than 11)
To calculate the probability of getting more than 11 successes, given that n = 13 and p = 0.75, we can use the binomial probability formula:
P(X > 11) = 1 - P(X ≤ 11)
Where:
- P(X > 11) is the probability of getting more than 11 successes.
- P(X ≤ 11) is the probability of getting 11 or fewer successes.
To calculate P(X ≤ 11), we need to calculate the cumulative binomial probability up to 11 and subtract it from 1.
The cumulative binomial probability can be calculated using the formula:
P(X ≤ k) = Σ(C(n,k) * p^k * (1-p)^(n-k))
Where:
- C(n,k) is the binomial coefficient which represents the number of ways to choose k successes from n trials.
- p is the probability of success in one trial.
- (1 - p) is the probability of failure in one trial.
- n is the number of trials.
- k represents the number of successes.
Let's start by calculating P(X ≤ 11).