Probability

Binomial Probability

Formula

P(X = k) = C(n, k) × pᵏ × (1−p)ⁿ⁻ᵏ

What is Binomial Probability?

The binomial probability formula gives the probability of exactly k successes in n independent trials, where each trial has a success probability p.

Variables

n
n — Number of trials
k
k — Number of successes
p
p — Probability of success on each trial
C
C(n, k) — Combinations of n items taken k at a time

Worked Examples

Example 1

A coin is flipped 5 times. What is the probability of getting exactly 3 heads?

Solution:

P = C(5,3) × (0.5)³ × (0.5)² = 10 × 0.125 × 0.25 = 0.3125

Frequently Asked Questions

Related Formulas

P(Event) = (Number of favorable outcomes) / (Total number of outcomes)

C(n, r) = n! / (r! × (n−r)!)

P(n, r) = n! / (n−r)!

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