Probability Basics
Grades 8–10 Probability Fractions
Probability puts a number on chance: 0 means impossible, 1 means certain, 1/2 means a coin flip.
P(event) = favorable outcomes ÷ total outcomes
Die rolls a 4 or 5: 2 favorable / 6 total = 1/3 ≈ 0.333
Bag: 3 red, 2 blue: P(red) = 3/5 = 0.6
The complement — "not" made easy
P(something happens) = 1 − P(it doesn't). Easier to compute the flip side: P(at least one six in 2 rolls) = 1 − P(no sixes).
AND multiplies, OR adds (carefully)
- AND (independent): P(A then B) = P(A) × P(B). Two coins, both heads: 1/2 × 1/2 = 1/4
- OR (can't both happen): P(A or B) = P(A) + P(B). Die shows 2 or 5: 1/6 + 1/6 = 1/3
Watch out
"OR" only adds cleanly when events can't overlap. P(king or heart)
is not 4/52 + 13/52 — the king of hearts was counted twice.
Subtract the overlap: 4/52 + 13/52 − 1/52 = 16/52.
Practice
P(coin lands heads) = ___
P(die shows exactly a 3) = ___
P(two dice both show sixes) = ___
P(rain) = 0.3 → P(no rain) = ___
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