Question

Match each equation with the correct type of probability?

Answer 1

Answers:

1. P(A or B) not mutually exclusive
2. P(A and B) not independent (aka dependent)
3. P(A and B) independent
4. P(A or B) mutually exclusive
5. 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.