Math & Statistics
Probability Calculator
Calculate probability, odds, and expected value for events.
Probability is the foundation of statistics, risk management, and rational decision-making. This calculator converts between probability formats and calculates odds and expected value.
Probability
5.7692%
- fraction
- 3/52
- decimal
- 0.057692
- odds
- 3:49 (for:against)
- expected Value
- $-3.65 EV per play
Formula and method
P = Favorable / Total; EV = P(win) × Payout - P(lose) × Cost
Classical probability theory. Expected value calculation shows the mathematical expectation per trial given equal odds of each outcome.
Worked examples
Drawing an ace from a deck
- Favorable Outcomes:
- 4
- Total Possible Outcomes:
- 52
- Payout if Wins ($):
- 100
- Cost to Play ($):
- 10
Probability: 7.6923%
Rolling a 6 on a die
- Favorable Outcomes:
- 1
- Total Possible Outcomes:
- 6
- Payout if Wins ($):
- 50
- Cost to Play ($):
- 5
Probability: 16.6667%
Assumptions and limits
- Equally likely outcomes
- Independent events
- Classical probability model
This tool provides an educational estimate. Rules, rates and personal circumstances can change the answer. Review the assumptions before relying on a result. Report a correction.
Common mistakes to avoid
- Confusing "or" and "and" probability — P(A or B) = P(A) + P(B) - P(A and B).
- Assuming independent events when they are dependent (drawing cards without replacement).
- Interpreting probability as frequency in a small sample — the law of large numbers requires many trials.
Frequently asked questions
What is expected value?
EV is the average outcome per trial over many repetitions. A positive EV means the activity is profitable on average. A negative EV (like most casino games) means you lose money on average long-term.
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