Coin flip probability basics
A fair coin has two equally likely outcomes, so the probability of heads on one flip is 1/2, or 50%. The same is true for tails. Each new flip is independent: earlier results do not change the odds of the next flip.
Probability of several coin flips
The number of possible ordered sequences doubles with every flip. Two flips have 2² = 4 sequences, three flips have 2³ = 8, and ten flips have 2¹⁰ = 1,024. Every particular sequence, such as HHTH, has the same probability as any other sequence of the same length.
How the calculator finds exactly k heads
There can be many sequences with the same total number of heads. The binomial coefficient counts those sequences. For a fair coin, the probability is:
P(exactly k heads) = C(n, k) ÷ 2n
Here, n is the number of flips, k is the target number of heads, and C(n, k) is the number of ways those heads can be arranged.
Common examples
- One head in one flip: 50%
- Two heads in two flips: 25%
- Exactly one head in two flips: 50%
- At least one head in three flips: 87.5%
- Exactly five heads in ten flips: about 24.61%
Test the probability yourself
Calculated probability describes what to expect across many repeated trials, not what must happen in the next batch. Use the multiple coin flipper to run an experiment, or return to the single online coin flip for a quick decision.
Frequently asked questions
What is the probability of heads twice in a row?
Multiply 1/2 by 1/2. The probability is 1/4, or 25%.
Do previous flips affect the next flip?
No. Independent fair coin flips have no memory. After ten tails in a row, the next flip still has a 50% chance of heads.
Why is exactly half heads not guaranteed?
Probability predicts a long-run pattern, not a required result in a small sample. Random variation can produce an uneven number of heads and tails.