How it's calculated
P(X = k) = C(n, k) · pᵏ · (1 − p)ⁿ⁻ᵏ
n = number of tosses, k = number of heads, p = probability of heads (0.5 for a fair coin), C(n,k) = binomial coefficient “n choose k”. Mean = n·p, variance = n·p·(1 − p).
Worked examples
| Flips | Heads (k) | P(X=k) | Note |
|---|---|---|---|
| 1 | 1 | 50% | Single fair flip |
| 2 | 2 | 25% | Two heads in a row |
| 10 | 5 | 24.6% | Most likely single outcome |
| 100 | 50 | 7.96% | Exactly half heads |
Common questions
What are the odds of 2 heads in a row?
With a fair coin the chance is 1 in 4, or 25 percent.
Why is exactly 50 heads in 100 flips so unlikely?
Even though 50 is the most probable single result, it competes with dozens of nearby outcomes, so its individual chance is only about 8 percent.