Sec. 5.2 Probability Rules
Probability Rules
A = Event
S = sample space
P(A) = probability of event A
P(S) = probability of S
1. Probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1.
*in the long run
2. If S is the sample space in a probability model, then P(S) = 1 (Probabilities of all outcomes must add up
to 1.)
3. The complement of any event A is the event A does not occur (AC).
Complement Rule states: P(AC) = 1 – P(A).
4. Events A & B are mutually exclusive (also known as disjoint) if they have no outcomes in common.
Addition Rule: P(A or B) = P(A) + P(B)
Example, p. 308
18 to 23
0.57
Age group (yr):
Probability:
24 to 29
0.17
30 to 39
0.14
40 or over
0.12
(a) Show that this is a legitimate probability model. Check to see that the probabilities add up to 1 and all are
between 0 and 1.
All between 0 and 1. 0.57 + 0.17 + 0.14 + 0.12 = 1.00 Legitimate probability model – YES!!!
(b) Find the probability that the chosen student is not in the traditional college age group (18 to 23 years)
Two ways: 1 – P(A) or add the probabilities of the remaining categories
1. 1 – 0.57 = 0.43
OR
2. 0.17 + 0.14 + 0.12 = 0.43
Notation:
***The UNION of two events means at least one of them happens (one or both)  OR
(A  B)
(A or B)
Ex. Rolling 2 dice
A = {roll doubles} = {1 1, 2 2, 3 3, 4 4, 5 5, 6 6}
B = {roll a sum of 6}
(A or B) = { 1 1, 2 2, 3 3, 4 4, 5 5, 6 6, 1 5, 2 4, 4 2, 5 1}
P(A or B) = 10/36 = 5/18 ≈ .278 = 27.8%
***The INTERSECTION of two events means both must occur.  AND
(A or B)
(A  B)
Ex. A = { roll doubles} = {1 1, 2 2, 3 3, 4 4, 5 5, 6 6}
B = {roll a double digit sum} = {4 6, 5 5, 5 6, 6 4, 6 5, 6 6}
(A and B) = {5 5, 6 6}
P(A and B) = 2/36 = 1/18 ≈ 0.055 = 5.6%
MUTUALLY EXCLUSIVE
Ex: A = {roll doubles} & B = {odd sum}
So P(A or B) = P(A) + P(B)
 6  18
36
36
 24
36
2

3
No outcomes alike
Event A = {1 1, 2 2, 3 3, 4 4, 5 5, 6 6} (6 outcomes)
Event B = {1 2, 1 4, 1 6, 2 1, 2 3, 2 5, 3 2, 3 4, 3 6, 4 1, 4 3
4 5, 5 2, 5 4, 5 6, 6 1, 6 3, 6 5} (18 outcomes)
THEN: (A and B) =  (or empty set)
IF:
A
B
Homework: p. 315 # 43, 45, 57, 59, 60