Math
Binomial probability.
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
Real-world.
- 1 Probability of getting exactly 3 heads in 5 coin flips: C(5,3)·(0.5)³·(0.5)² = 10/32 = 5/16
- 2 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