Binomial probability

Math

Definition

The probability of getting exactly k successes in n independent trials, each with success probability p. Calculated using the binomial probability formula involving combinations.

Examples

  • Probability of getting exactly 3 heads in 5 coin flips: C(5,3)·(0.5)³·(0.5)² = 10/32 = 5/16
  • Probability that exactly 2 out of 10 free throws are missed if a player makes 80% of shots
Key Fact

P(X = k) = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ

Related Terms

Binomial distribution Permutations and combinations Basic probability Geometric distribution

Study This Concept

Practice binomial probability with free review games in these units:

Algebra 2 Unit 10: Probability and Statistics