Download AP Statistics Notes 5.2 Vocabulary: Sample space – S – set of all

AP Statistics
Notes 5.2
Vocabulary:
Sample space – S – set of all possible outcomes
1 coin S = {H,T}
1 die S = {1, 2, 3, 4, 5, 6}
Event – any outcome or set of outcomes
Addition rule for mutually exclusive events: If two events have no outcomes in common and so can
never occur simultaneously, the probability that one or the other occurs is the sum of their individual
probabilities. (also called mutually exclusive events or disjoint events)
P(A or B) = P(A) + P(B)
P(A ∪ B) = P(A) + P(B)
Example:
Randomly select a student who took the 2010 AP Statistics exam and record the student’s score. Here
is the probability model:
Score
Probability
1
0.233
2
0.183
3
0.235
4
0.224
1. Show that this is a legitimate probability model.
2. Find the probability that the chosen student scored 3 or better.
5
0.125
Two-Way Tables and Probability
A random sample of 500 people who participated in the 2000 census was chosen. Each member of the
sample was identified as a high school graduate (or not) and as a home owner (or not). The two-way
table displays the data.
Homeowner
Not a homeowner
Total
High
school
graduate
221
89
310
Not a
high
school
graduate
Total
119
340
71
160
190
500
Suppose we choose a member of the sample at random. Find the probability of each of the following.
3. P(high school graduate)
4. P(high school graduate and owns a home)
5. P(high school graduate or owns a home)
6. Why can’t we use the addition rule in the previous problem?
General Addition Rule for Two Events: If A and B are any two events resulting from some chance
process, then
P(A or B) = P(A) + P(B) – P(A and B)
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Venn diagram:
Let A = high school graduate
Let B = owns home
7. P(A ∪ B)
8. P(A ∩ B)
9. P(A ∩ Bc)
10. P(Ac ∩ B)
11. P(Ac ∩ Bc)
According to the National Center for Health Statistics, in December 2008, 78% of U.S. households had
a traditional landline telephone, 80% of households had cell phones, and 60% had both. Suppose we
randomly selected a household in December 2008.
12. Make a two-way table that displays the sample space of this chance process.
13. Construct a Venn diagram to represent the outcomes of this chance process.
14. Find the probability that the household has at least one of the two types of phones.
15. Find the probability that the household has a cell phone only.