STA020 · Probability & statistics · Classes 11–12
Conditional probability
Conditional probability P(A | B) is the chance of A when we already know B happened: only the outcomes in B count.
P(A | B)Conditional probability
📐 Formula
P(A | B) = P(A ∩ B) / P(B)
✏️ Worked example
Given the first die shows 4 (the blue column), P(sum ≥ 8) = 3/6, since the second die must be 4, 5 or 6.
🌍 Where it is used
Medical tests, weather given clouds, cricket chances given the score.
❓ Quick check
A bag has 3 red, 2 blue. One red is removed. P(next is red)?
🏋️ Practice
EasyGiven a die is even, P(it is 6)?
Answer: 1/3
MediumP(A ∩ B) = 0.2, P(B) = 0.5. P(A | B)?
Answer: 0.4
ChallengeIndependent events: P(A | B) = ?
Answer: P(A)