Coin Flip Probability Calculator

Coin Flip Probability is evaluated from Number of Flips and Desired Number of Heads. The calculation reports P, P and P.

Results

Thanks — we’ve logged this for review.

About the Coin Flip Probability Calculator

Coin Flip Probability is treated here as a quantitative relation between Number of Flips and Desired Number of Heads and P, P, P and Expected Heads.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
P(exactly k heads) = C(n,k) x 0.5^n.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

P(exactly k heads) = C(n,k) x 0.5^n.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: 10 coin flips: P(exactly 7 heads)

Inputs

n_flips: 10 k_heads: 7
P: 0.117188. P: 0.945313. P: 0.171875. Expected Heads: 5. Std Dev): 1.5811

With Number of Flips = 10 and Desired Number of Heads = 7 as the stated inputs, the result is P = 0.117188, P = 0.945313 and P = 0.171875. Each value corresponds to the declared output fields.

Example 2: 20 flips: P(exactly 10 heads — perfect balance)

Inputs

n_flips: 20 k_heads: 10
P: 0.176197. P: 0.588099. P: 0.588099. Expected Heads: 10. Std Dev): 2.2361

With Number of Flips = 20 and Desired Number of Heads = 10 as the stated inputs, the result is P = 0.176197, P = 0.588099 and P = 0.588099. Each value corresponds to the declared output fields.

Example 3: 100 flips: P(at least 60 heads)

Inputs

n_flips: 100 k_heads: 60
P: 0.010844. P: 0.9824. P: 0.028444. Expected Heads: 50. Std Dev): 5

With Number of Flips = 100 and Desired Number of Heads = 60 as the stated inputs, the result is P = 0.010844, P = 0.9824 and P = 0.028444. Each value corresponds to the declared output fields.

Example 4: NBA playoff: If two equal teams, P(6-game series with better team winning 4 of 6)

Inputs

n_flips: 6 k_heads: 4
P: 0.234375. P: 0.890625. P: 0.34375. Expected Heads: 3. Std Dev): 1.2247

With Number of Flips = 6 and Desired Number of Heads = 4 as the stated inputs, the result is P = 0.234375, P = 0.890625 and P = 0.34375. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate probability of k heads in n coin flips
  • Understand binomial distribution
  • Random tie-breaking and fairness in probability