# If p is the probability of success of a binomial experiment, what is the probability of failure?

The sum of probabilities of success and failure is always one in a binomial expression.

## Answer: The probability of failure, when the probability of success is p, is 1 - p.

Go through the explanation to understand better.

**Explanation:**

In a binomial experiment, probability of success + probability of failure = 1

Let us suppose the probability of failure to be q. Hence, an expression can be formed as:

⇒ p + q = 1

⇒ q = 1 - p

Example:

1) If the probability of success for an event is 1/10, calculate the probability of failure for the same event is:

Probability of failure = 1 - the probability of success

Probability of failure = 1 - 1/10 = 9/10

### Thus, the probability of failure, when the probability of success is p, is 1 - p.

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