Coin Toss Probability Calculator
Calculate the probability of getting exactly k heads in n fair coin tosses.
Inputs
0.5 for fair coin
P(exactly k heads)
0.24609375
P(≥ k heads)
0.62304688
P(≤ k heads)
0.62304688
Step by step
Values used
Number of Tosses = 10; Desired Heads = 5; P(Heads) per toss = 0.5000
Formula applied
P(k heads in n tosses) = C(n,k) × p^k × (1−p)^(n−k)
P(exactly k heads)
= 0.24609375
P(≥ k heads)
= 0.62304688
P(≤ k heads)
= 0.62304688
How it works
Coin toss probability is a direct application of the binomial distribution. With n independent tosses each having probability p of heads, the probability of exactly k heads is C(n,k) × p^k × (1−p)^(n−k).
Formula
P(k heads in n tosses) = C(n,k) × p^k × (1−p)^(n−k)
- n
- Number of tosses
- k
- Desired heads
- p
- Probability of heads per toss
Frequently Asked Questions
What is the probability of getting 5 heads in 10 fair coin flips?
C(10,5) × 0.5^10 = 252/1024 ≈ 0.2461 or about 24.6%.
Is each toss truly independent?
For a fair coin, yes. Previous outcomes do not affect future ones — this is the gambler's fallacy.