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Card Odds
Estimate the chance of a card event. Compete on the accuracy of your probability judgment.
MO STATS · FREE CALCULATOR
Binomial Probability Calculator
Find the probability of a number of successes across independent trials with the same success probability.
No account to calculateNo real-money wageringTransparent assumptions
CALCULATOR
Binomial probability
Find the probability of a number of successes across independent repeated trials.
Start with your assumptions
Enter values and calculate to see the result, method, and assumptions.
PUT YOUR JUDGMENT TO WORK
Compete on decisions.
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Worked example
- Exactly 6 successes
- 20.5078%
- At least 6 successes
- 37.6953%
- At most 6 successes
- 82.8125%
In 10 independent fair coin flips, the probability of exactly 6 heads is C(10,6) × 0.5¹⁰ = 210 ÷ 1024 = 20.5078%. “At least 6” adds the probabilities for 6 through 10 heads.
Example inputs
- n:
10 - p:
0.5 - k:
6
Method
P(X = k) = C(n,k)pᵏ(1 − p)ⁿ⁻ᵏ. Cumulative probabilities sum the appropriate outcomes. The implementation constructs a normalized distribution using recurrence from its mode to avoid overflowing combinatorial coefficients.
Assumptions
Each trial is independent, has the same success probability, and has two possible classifications. Draws from a finite deck without replacement do not meet these assumptions; use the card draw calculator for that setting.
Related
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