Probability Rules - Lecture Slides | STAT 101, Study notes of Statistics

Material Type: Notes; Class: PRIN OF STATISTICS; Subject: STATISTICS; University: Iowa State University; Term: Unknown 1989;

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Stat 101L: Lecture 22
1
1
Probability Rules
In Chapter 14 we were
introduced to some simple rules
of probability in Chapter 15 we
will look at more general rules.
2
Surviving the Titanic
2223710285329899
1517536166130685
Lost
706174119199214
Saved
TotalSteerageSecondFirstCrew
3
Probability of Surviving
If we select an individual at
random from the Titanic, what
is the chance that individual
survived?
Each individual has an equal
chance of being selected.
pf3
pf4
pf5

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1

Probability Rules

In Chapter 14 we were

introduced to some simple rules

of probability in Chapter 15 we

will look at more general rules.

2

Surviving the Titanic

899 329 285 710 2223

Lost 685 130 166 536 1517

Saved 214 199 119 174 706

Crew First SecondSteerage Total

3

Probability of Surviving

If we select an individual at

random from the Titanic, what

is the chance that individual

survived?

Each individual has an equal

chance of being selected.

4

Formal Probability

( ) Total ofoutcomes

ofoutcomesinEvent Event #

P =

5

Probability of survival

Probability individual selected

was saved

–706/2223=0.318 or 31.8%

Probability individual selected

was lost

–1517/2223=0.682 or 68.2%

6

General Addition Rule

P(A or B) = P(A) + P(B)

  • P(A and B) P(Saved or First Class) = P(Saved) + P(First Class) – P(Saved and First Class) = 706/2223 + 329/2223 – 199/ = 0.376 or 37.6%

10

General Multiplication Rule

P(A and B) = P(A)P(B|A) P(First Class and Saved) = P(First Class)P(Saved|First Class) = (329/2223)*0.605 = 0.09 or 9% P(First Class and Saved) = 199/2223 = 0.09 or 9%

11

Independent Events

Two events are independent if the probability of the occurrence of one event does not effect nor is it affected by the occurrence of the other event. P(A) = P(A|B) = P(A|B C^ )

12

Not independent events

Saved and First Class are not

independent events because:

–P(Saved) = 0. –P(Saved|First Class) = 0. –The two probabilities are not equal.

13

Independent Trials

Sampling with replacement

creates independent trials.

–P(Red on 1 st^ and Red on 2 nd)= P(Red on 1 st^ )P(Red on 2 nd)

14

Dependent Trials

Sampling without replacement

creates dependent trials.

–P(Red on 1 st^ and Red on 2 nd)= P(Red on 1 st)P(Red on 2 nd^ |Red on 1 st)

15

Tree diagram

1 st^ Trial 2 nd^ Trial Red Red White Blue Red White White Blue Red Blue White Blue