Enter the total number of trials, number of successful trials, and the probability of success on a single trial into the calculator to determine the probability of success after N trials.
Probability Of Success After N Trials Formula
The following formula is used to calculate the probability of success after N trials.
P(X=k) = C(n, k) * (p^k) * ((1-p)^{(n-k)})Variables:
- P(X=k) is the probability of success after N trials
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success on a single trial (decimal)
What is a Probability Of Success After N Trials?
The Probability of Success After N Trials, often referred to in statistics as the binomial probability, is the likelihood of achieving a specific number of "successes" in a set number of trials or attempts. A "success" is defined as the outcome that we are interested in. This concept is used in binomial experiments where each trial is independent and has only two possible outcomes - success or failure. The probability remains constant throughout all trials.
How to Calculate Probability Of Success After N Trials?
The following steps outline how to calculate the Probability Of Success After N Trials using the given formula:
- First, determine the values of p, n, and k.
- Next, calculate the combination C(n, k) using the formula C(n, k) = n! / (k! * (n-k)!), where "!" denotes factorial.
- Then, calculate p^k, where "^" denotes exponentiation.
- Next, calculate (1-p)^(n-k).
- Finally, multiply C(n, k), p^k, and (1-p)^(n-k) to get the Probability Of Success After N Trials.
Example Problem:
Use the following variables as an example problem to test your knowledge:
p = 0.6
n = 5
k = 3
