Answers:
- P(A or B) not mutually exclusive
- P(A and B) not independent (aka dependent)
- P(A and B) independent
- P(A or B) mutually exclusive
- P(A | B)
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Explanation:
The formula we use for "or" cases is
P(A or B) = P(A) + P(B) - P(A and B)
If events A and B are mutually exclusive, then we ignore the P(A and B) part since that is 0. Mutually exclusive events cannot occur simultaneously, which is why we have that 0.
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For "and" cases, we have two basic flavors
P(A and B) = P(A)*P(B | A)
P(A and B) = P(B)*P(A | B)
We go with the first case for problem 2. These formulas apply if A and B are not independent.
If they are independent, then
P(A and B) = P(A)*P(B)
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Start with the equation P(A and B) = P(B)*P(A | B) and divide both sides by P(B).
You'll end up with
P(A | B) = P(A and B)/P(B)
which is a conditional probability.
