The binomial distribution is an independent Bernoulli test repeated n times. There are only two possible results in each experiment. Whether these two results are mutually opposite and independent has nothing to do with the results of other experiments. The probability of events remains constant in each independent experiment, so this series of experiments is called N-fold Bernoulli experiment. When the number of tests is 1, the binomial distribution is Bernoulli distribution.

1. There are only two possible results in each experiment, and they are opposite to each other;

2. Each experiment is independent and has nothing to do with the results of other experiments;

3. The probability of the obtained events remains unchanged in the whole series of experiments, so this series of experiments is called Bernoulli experiment.

In this test, the number of events is random and follows binomial distribution, so binomial distribution can be used for reliability test. Reliability tests are often conducted with n identical modes for t hours, and only k modes are allowed to fail. The probability of passing the test can be obtained by applying binomial distribution.

If the probability of an event is p and the experiment is repeated n times, the probability of an event happening k times is:

P = C(n, k) × p k × (1-p) (n-k), where C(n, k) represents the number of combinations.