PROBABILITY: Ch 11

1
PROBABILITY Ch 11

• I. Rule of Addition
• II. Rule of Multiplication
• III. Bayes Rule

2
I.Rule of Addition
3
Rule of Addition

• P(J or A) P(J or A or both)
  P(J) P(A) P(A and J)
  .7 .8 - .6 .9

4
.1 .6 .2 .1

• J A
  
• P(J or A) .1 .6 .2 .9

5
Mutually Exclusive
6
Mutually Exclusive

• P(A or B) P(A) P(B) Special Case

7
II. Rule of Multiplication

• P(A and J) P(AJ)P(J), where P(AJ) P(A given
  J)

8
Conditional Probability

• P(AJ) P(acceptable, given made in Japan)

9
(No Transcript)
10
.6/.7.86
11
Independence

• New Example 2
  machines(I and II)

12
Independence
13
Special Case of Rule of Multiplication

• P(A and I) P(A)P(I) (.9)(.8) .72

14
P(acceptable, given Machine I) P(acceptable)
15
P(AI) .72/.80 .90 P(A)
16
Return to First Example

• P(acceptable) depended on Japan vs US

17
Dependence

• Acceptable and Japan were dependent events

18
III. Bayes Rule

• Alternative Conditional Probability

19
Bayes Rule Example

• D Drop in stock market
• I Increase in oil price
• Prior probability P(D) .8
• ComplementP(D).2
• Conditional probability In the past, 3 out of 4
  years when stock market dropped, oil prices had
  increased the previous year. P(ID) .75

20
Bayes Rule Continued

• For those years when the stock market did not
  drop, half of the previous years had price
  increases. Complement of D D. P(ID) .5
• QUESTION If oil prices increase this year, find
  the probability that the stock market drops next
  year.

21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
.6/.7 .86

• If oil prices increase, .86 probability of drop
  in stock prices