Probability Calculator
Compute probabilities three ways: the binomial chance of exactly/at least/at most k heads in n coin flips, single-die roll odds against any target, or a custom favorable-over-total event. Each result lands on a color-coded likelihood band.
TheCalculators — Probability Calculator
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P(exactly 5 heads in 10 flips)
24.6094%
C(10,5) ÷ 2^10 = 252 ÷ 1,024
- Flips (n)
- 10
- Target heads (k)
- 5
- P(exactly k)
- 24.6094%
- P(at most k)
- 62.3047%
- P(at least k)
- 62.3047%
- Equally likely outcomes
- 1,024
- Odds for exactly k
- 3.06 : 1 against
Binomial probability, step by step
- 1Count outcomesn flips have 2^10 = 1,024 equally likely head/tail sequences
- 2Count favorablesequences with exactly 5 heads: C(10,5) = 252
- 3DivideP = 252 ÷ 1,024 = 0.246094 = 24.6094%
- 4CumulativeP(at most 5) sums C(10,i) for i ≤ 5 → 62.3047%; P(at least 5) → 62.3047%
Likelihood of exactly k heads
0.2
Unlikely
Most useful next
Formula
P(event) = favorable outcomes ÷ total outcomes · Coin: P(k heads) = C(n,k) ÷ 2ⁿ
Pro tips
- • Probabilities always live between 0 (impossible) and 1 (certain) — the color band shows where your event sits.
- • For coins, “at least k” and “at most k−1” are complements: their probabilities add to exactly 1.
- • The custom mode is the universal definition — any experiment with equally likely outcomes can use it.
FAQ
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