1. Probability: Summary of Rules
Rule 1: Complement Rule P(A) + P(Ac) = 1 if Ac represents the complement of A Rule 2B: Additive Rule P(A or B) = P(A) + P(B) if Events A and B are mutually exclusive Note: two events that are complements are always mutually exclusive Rule 3B: Multiplication Rule P(A and B) = P(A)×P(B) if Events A and B are independent

2. Clicker Quiz #8
Maria wants to take French or Spanish, or both. But classes are closed, ands he must apply to enroll in a language class. She has a 60% chance of being admitted to French, a 50% chance of being admitted to Spanish, and a 20% chance of being admitted to both French and Spanish.
P(French or Spanish) = _____________________
= _______
= _____
P(French) +P(Spanish) – P(both)
– 0.2
0.9
The events “admitted to French” and “admitted to Spanish” are:
Mutually exclusive but not independent
Independent but not mutually exclusive
Both mutually exclusive and independent
Neither mutually exclusive nor independent

3. With 50 people in the room…
There are 49 possible pairs with me.
P(No match with my birthday) = (364/365)49 = 0.874
There are …+1 = 1225 total possible pairs.
P(No match at all) = .030
and we can estimate by (364/365)1225 = .035

4. Probability review
Suppose we roll two fair dice, one red and one blue.
Let the event A be that we roll the same number on both dice.
Let the event B be that the sum of the two dice is even.
What is P(A)?
What is P(B)?
What is P(A and B)?
What is P(A or B)?
Ans: 6/36 or 1/6
Ans: 18/36 or 1/2
Ans: 1/6 (Note: NOT independent)
Ans: 1/2 (Note: NOT mutually exclusive)

5. More probability review
Suppose that you roll a fair 6-sided die until the first occurrence of a 4.
What is the probability that the first 4 occurs on the third roll?
1/6
5/6
(5/6) × (5/6) × (1/6)
(1/6) × (1/6) × (1/6)
(1/6) + (1/6) + (1/6)