1. Compare “A and B” to “A or B”
The compound event “A and B” means that A and B both occur in the same trial. Use the multiplication rule to find P(A and B).
The compound event “A or B” means either A can occur without B, B can occur without A or both A and B can occur. Use the addition rule to find P(A or B). A B A B
A or B
A and B

2. Mutually Exclusive Events
Two events, A and B, are mutually exclusive if they cannot occur in the same trial.
A = A person is under 21 years old
B = A person is running for the U.S. Senate
A = A person was born in Philadelphia
B = A person was born in Houston A
Mutually exclusive B
P(A and B) = 0
When event A occurs it excludes event B in the same trial.

3. Non-Mutually Exclusive Events
If two events can occur in the same trial, they are non-mutually exclusive.
A = A person is under 25 years old
B = A person is a lawyer
A = A person was born in Philadelphia
B = A person watches West Wing on TV
A and B
Non-mutually exclusive
P(A and B) ≠ 0 A B

4. The Addition Rule
The probability that one or the other of two events will occur is: P(A) + P(B) – P(A and B)
A card is drawn from a deck. Find the probability it is a king or it is red.
A = the card is a king B = the card is red.
P(A) = 4/52 and P(B) = 26/52
but P(A and B) = 2/52
P(A or B) = 4/ /52 – 2/52
= 28/52 = 0.538

5. When events are mutually exclusive,
The Addition Rule
A card is drawn from a deck. Find the probability the card is a king or a 10.
A = the card is a king B = the card is a 10.
P(A) = 4/52 and P(B) = 4/52 and P(A and B) = 0/52
P(A or B) = 4/52 + 4/52 – 0/52 = 8/52 = 0.054
When events are mutually exclusive,
P(A or B) = P(A) + P(B)

6. Contingency Table One of the responses is selected at random. Find:
The results of responses when a sample of adults in 3 cities was asked if they liked a new juice is:
Omaha
Seattle
Miami
Total
Yes
100
150
150
400 No
125
130 95
350
Undecided 75
170 5
250
Total
300
450
250
1000
One of the responses is selected at random. Find:
1. P(Miami and Yes)
2. P(Miami and Seattle)
3. P(Miami or Yes)
4. P(Miami or Seattle)

7. Contingency Table 1. P(Miami and Yes) 2. P(Miami and Seattle) = 0
Omaha
Seattle
Miami
Total
Yes
100
150
150
400 No
125
130 95
350
Undecided 75
170 5
250
Total
300
450
250
1000
One of the responses is selected at random. Find:
1. P(Miami and Yes)
2. P(Miami and Seattle)
= 250/1000 • 150/250 = 150/1000 = 0.15
= 0

8. Contingency Table 3 P(Miami or Yes) 4. P(Miami or Seattle) Omaha
Total
Yes
100
150
150
400 No
125
130 95
350
Undecided 75
170 5
250
Total
300
450
250
1000
3 P(Miami or Yes)
4. P(Miami or Seattle)
250/ /1000 – 150/1000
= 500/1000 = 0.5
250/ /1000 – 0/1000
= 700/1000 = 0.7

9. P(A and B) = P(A) • P(B|A) P(A or B) = P(A) + P(B) - P(A and B)
Summary
For complementary events P(E') = 1 - P(E)
Subtract the probability of the event from one.
The probability both of two events occur
P(A and B) = P(A) • P(B|A)
Multiply the probability of the first event by the conditional probability the second event occurs, given the first occurred.
Probability at least one of two events occur
P(A or B) = P(A) + P(B) - P(A and B)
Add the simple probabilities, but to prevent double counting, don’t forget to subtract the probability of both occurring.