In a binomial experiment, there are only two possible outcomes for each trial: success and failure. If we denote the probability of success as p, then the probability of failure can be determined using the complementary relationship between success and failure.
The sum of the probabilities of all possible outcomes must equal 1. Therefore, if the probability of success is p, the probability of failure, denoted as q, can be calculated using the formula:
q = 1 – p
For example, if the probability of success p is 0.7, then the probability of failure would be:
q = 1 – 0.7 = 0.3
This means that in a binomial experiment where the chance of success is 70%, the chance of failure is 30%.