Probability of Error Calculator

Formula

The formula to calculate the Probability of Error (PE) is:

\[ PE = C(n, k) \cdot p^k \cdot (1-p)^{(n-k)} \]

Where:

\( PE \) is the probability of error.
\( C(n, k) \) is the combination of \( n \) trials taken \( k \) at a time.
\( p \) is the probability of success on a single trial.
\( k \) is the number of successful trials.
\( n \) is the total number of trials.

Example

Let's say the total number of trials (\( n \)) is 10, the number of successful trials (\( k \)) is 3, and the probability of success on a single trial (\( p \)) is 0.5. Using the formula:

\[ PE = C(10, 3) \cdot 0.5^3 \cdot (1-0.5)^{(10-3)} = 120 \cdot 0.125 \cdot 0.0078125 \approx 0.117 \]

So, the Probability of Error (\( PE \)) is approximately 0.117.

What is Probability Of Error?

Probability of error is the likelihood that a given number of successes will not occur in a series of trials, given a certain probability of success on each trial. It is a key concept in statistics and probability theory, often used to assess the risk or uncertainty associated with a process or experiment.