Practice question · Fill in the blanks
Complete the relationship between the two most-confused notions.
Two events with positive probability that are mutually exclusive must be ______.
Word bank: dependent · independent · equally likely · complementary
Hints
- If one of them happens, what do you now know about the other?
- Knowing something for certain is the strongest possible change in probability.
Show the answer
Two events with positive probability that are mutually exclusive must be dependent.
Why
If A occurs, B is ruled out entirely, so P(B given A) = 0, which is not P(B) unless B was impossible to begin with. Learning that one occurred changes the other's probability as much as it possibly could, that is extreme dependence, the opposite of independence.
Practise Conditional Probability and Independence
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