1. Homework: pg.440 A B
0.056
0.082
0.179
66.) ) A. Household is prosperous and educated=0.082 B. Household is prosperous but not educated=0.056 C. Household is not prosperous but is educated=0.179 D. Household is neither prosperous nor educated=.683
0.683

2. 69.) A. 15% B. 20% 70.) A. B. 0.3 C. 0.4 Coffee only 0.2 Tea only 0.05
Cola only
0.15
0.1
69.) A. 15% B. 20% 70.) A. B. 0.3 C. 0.4
0.20
Gospel
Country
0.2
0.1
0.3
0.4

3. 6.3 Conditional Probability

4. Intro Example: P(Ace, then Jack)= Without replacement
Given that you got an Ace, P(Jack)

5. Conditional Probability
Notation:
Words:
Probability of B given A

6. Example:
Neither Parent Smokes
One Parent Smokes
Both Parents Smokes
Total
Student Does not Smoke
1168
1823
1380
4371
Student Smokes
188
416
400
1004
1356
2239
1780
5375
Let A= Student Smokes
B=One parent smokes

7. Example continued
Are A and B disjoint? Independent? P(A)= P(A and B)= P(A or B)= P(B|A)=
Let A= Student Smokes
B=One parent smokes
Neither Parent Smokes
One Parent Smokes
Both Parents Smokes
Total
Student Does not Smoke
1168
1823
1380
4371
Student Smokes
188
416
400
1004
1356
2239
1780
5375

8. General Multiplication Rule
For any two events:
P(A and B)= P(A) * P(B|A)
Also, P(B|A)=

9. Back to Smoking Example:
Find P(B|A) using the formula
Neither Parent Smokes
One Parent Smokes
Both Parents Smokes
Total
Student Does not Smoke
1168
1823
1380
4371
Student Smokes
188
416
400
1004
1356
2239
1780
5375

10. Independence Rule
If , then events A and B are independent.
Proof:

11. Are A and B independent?
Neither Parent Smokes
One Parent Smokes
Both Parents Smokes
Total
Student Does not Smoke
1168
1823
1380
4371
Student Smokes
188
416
400
1004
1356
2239
1780
5375
Let A= Student Smokes
B=One parent smokes

13. Homework: pg. 446 # 74, 78 pg. 451 #79