How to Calculate Probability: Basic Formulas and Examples

By Jorge Sanchez · April 20, 2026 · 6 min read

Bottom line: P(event) = Number of favorable outcomes ÷ Total number of outcomes. Probability always falls between 0 (impossible) and 1 (certain). A 50% chance = 0.5.

Basic Probability Formula

P(A) = Number of favorable outcomes ÷ Total possible outcomes

Examples:

Rolling a 4 on a standard die: P = 1/6 ≈ 16.7%
Drawing an ace from a deck: P = 4/52 = 1/13 ≈ 7.69%
Flipping heads on a coin: P = 1/2 = 50%
Drawing a red card: P = 26/52 = 1/2 = 50%

AND Probability (Both Events Occur)

For independent events (one doesn't affect the other):

P(A and B) = P(A) × P(B)

Example: What's the probability of flipping heads twice in a row?

P(H and H) = 0.5 × 0.5 = 0.25 = 25%

Example: Rolling a 6 on each of two dice?

P(6,6) = 1/6 × 1/6 = 1/36 ≈ 2.78%

OR Probability (At Least One Event Occurs)

For mutually exclusive events (can't both happen):

P(A or B) = P(A) + P(B)

For non-mutually exclusive events (can both happen):

P(A or B) = P(A) + P(B) − P(A and B)

Example: Drawing a king or a heart from a deck?

P(King) = 4/52, P(Heart) = 13/52, P(King of Hearts) = 1/52
P(King or Heart) = 4/52 + 13/52 − 1/52 = 16/52 ≈ 30.8%

Complement Rule (Probability Something Does NOT Happen)

P(not A) = 1 − P(A)

Example: What's the probability of NOT rolling a 1 on a die?

P(not 1) = 1 − 1/6 = 5/6 ≈ 83.3%

Conditional Probability

P(A|B) = "Probability of A given that B has already occurred."

P(A|B) = P(A and B) ÷ P(B)

Example: A bag has 3 red and 2 blue balls. You draw one ball — it's red. What's the probability the next draw is also red?

After removing 1 red, 2 red remain out of 4 total.
P(red | first was red) = 2/4 = 50%

Converting Between Formats

Format	Example	Meaning
Fraction	3/10	3 out of 10
Decimal	0.30	Divide fraction
Percentage	30%	Decimal × 100
Odds for	3:7	Favorable : Unfavorable

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Jorge Sanchez · Live Event Production Specialist · CalQpro