Lesson 24 of 1524
Probability topics
Subtract the overlap, and multiply only when the events are independent.
Practice this chapterAn event is a set of outcomes. Its probability is between 0 and 1, and the complement is 1 minus that probability.
The general addition rule subtracts the overlap so it is not counted twice. Conditional probability reads “given.” Independent events satisfy P(A and B) = P(A)P(B). A contingency table holds the counts these rules use.
Addition with an overlap
P(A or B) = P(A) + P(B) − P(A and B)
If the events cannot happen together, the overlap is 0 and you just add.
Worked example
P(A) = 0.3, P(B) = 0.4, and the events are mutually exclusive. What is P(A or B)?
- 1“A or B” uses the addition rule: P(A or B) = P(A) + P(B) − P(A and B).
- 2Mutually exclusive means A and B cannot happen together, so the overlap P(A and B) is 0.
- 3Substitute: 0.3 + 0.4 − 0 = 0.7.
- 4The subtraction is there so an overlap is not counted twice. Here the overlap is already 0, so subtracting it changes nothing.
Result: 0.7
Why. You add 0.3 and 0.4 because the two events share no outcomes. If they overlapped, part of that sum would have been counted twice, and you would subtract the shared probability. 0.7 is still between 0 and 1, so it can be a probability.
“Mutually exclusive” does not mean “independent.” If two events cannot happen together and both have positive probability, they are dependent.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.