Binomial probability calculates the probability of exactly k successes in n independent Bernoulli trials.
⚠p must be between 0 and 1, k must be between 0 and n.
What is Binomial Probability?
The binomial distribution models the number of successes in a fixed number of independent trials, each with two possible outcomes (success or failure) and constant probability of success.
Conditions
Fixed n, independent trials, two outcomes, constant p
Binomial probability calculates the probability of exactly k successes in n independent trials, each with success probability p. P(X=k) = C(n,k) × p^k × (1-p)^(n-k).
What are the requirements for binomial distribution?▼
Fixed number of trials, independent trials, two possible outcomes (success/failure), constant probability of success for each trial.
What is expected value of binomial distribution?▼
E[X] = n × p. The expected number of successes is the number of trials times the probability of success.
What is variance of binomial distribution?▼
Var(X) = n × p × (1-p). Standard deviation = sqrt(n × p × (1-p)).
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