Binomial probability distribution
Compute P(X = k) for a binomial random variable with n independent trials and success probability p. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Owen flips a fair coin 4 times. What is the probability that exactly 4 of the flips land heads?
P(X = 4) = C(n, k) · pk · (1 - p)n - k
n = 4, p = 12, k = 4
Answer: 1/16
See one solved, step by step
Aaliyah rolls a standard six-sided die 5 times. What is the probability that exactly 3 of the rolls come up 6?
P(X = 3) = C(n, k) · pk · (1 - p)n - k
n = 5, p = 16, k = 3
📘 Worked solution
1n = 5 trials, p = P(rolling a 6) = 16, k = 3.Identify the binomial parameters: number of trials, success probability, and the number of successes you want.
2C(5, 3) = 10This counts how many different orders the 3 successes could happen in among the 5 rolls.
3P(X = 3) = 10 · (16)3 · (56)2Multiply by p raised to the number of successes and (1 - p) raised to the number of failures.
4= 2507776 = 1253888Simplify the fraction to lowest terms.
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