Practice question · Fill in the blanks
Complete the condition under which probabilities may simply be added.
P(A) + P(B) gives P(A or B) only when the two events are ______.
Word bank: mutually exclusive · independent · equally likely · complementary
Hints
- Ask what goes wrong when the two events share an outcome.
- The third Kolmogorov axiom carries a condition, and that condition is the answer.
Show the answer
P(A) + P(B) gives P(A or B) only when the two events are mutually exclusive.
Why
Only disjoint events can be added directly; otherwise their shared outcomes are counted twice. Independence is a different condition entirely, it licenses multiplication, not addition, and is nearly the opposite of mutual exclusivity.
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