Two events are independent if one does not change the chance of the other, like two dice. Then P(A and B) = P(A) × P(B). P(at least one six) with two dice = 1 − P(no sixes) = 1 − 25/36 = 11/36.
To test independence, check whether P(A) × P(B) equals P(A ∩ B). Mutually exclusive events cannot happen together, so for them P(A or B) = P(A) + P(B). For events that can overlap, subtract the overlap.
Worked example
P(A) = 1/2, P(B) = 1/5 and P(A ∩ B) = 1/10. Are A and B independent?
- P(A) × P(B) = 1/2 × 1/5 = 1/10.
- This equals P(A ∩ B).
Answer:Yes, they are independent.
Key words
- independent
- one does not affect the other
- mutually exclusive
- cannot happen together
- at least one
- 1 − P(none)
Practise this
New questions every time.
Common Core-referenced: HSS-CP.B.7