Probability Rules

Adding, multiplying, and knowing which.

11 problems · about 24 minutes · AP Statistics 4.4, 4.5, 4.6

What this lesson teaches

The student applies the addition and multiplication rules and tests independence.

The addition rule subtracts the overlap so it is not counted twice.
The multiplication rule uses a conditional probability unless the events are independent.
Mutually exclusive is the opposite of independent, not a version of it.

Straightforward practice. Get the method working first.

4 problems

Independent, P(A) = 0.4, P(B) = 0.5. P(A and B)?
Answer 0.2
Why 0.2.
Independent, P(A) = 0.2, P(B) = 0.5. P(A and B)?
Answer 0.1
Why Multiply.
Mutually exclusive, P(A) = 0.3, P(B) = 0.4. P(A or B)?
Answer 0.7
Why No overlap to subtract.
Mutually exclusive events. What is P(A and B)?
Answer 0
Why They cannot both happen.

The same ideas with more to keep track of.

3 problems

P(A) = 0.6. What is P(not A)?
Answer 0.4
Why Everything sums to 1.
P(B|A) = P(B). Independent? 1 for yes, 0 for no.
Answer 1
Why Knowing A changed nothing.
Are mutually exclusive events independent? 1 for yes, 0 for no.
Answer 0
Why One happening rules the other out entirely.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Two fair coins. P(both heads)?
Answer 0.25
Why Half times half.
Select every statement that is always true.
Answer Every probability lies between 0 and 1.; All outcomes together sum to 1.
Why The addition rule needs the overlap subtracted.
Or: P(A) = 0.3, P(B) = 0.5, P(A and B) = 0.1. What is P(A or B)?
Answer 0.7
Why 0.7.
And: Independent events with P(A) = 0.5 and P(B) = 0.6. What is P(A and B)?
Answer 0.3
Why 0.3.