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Probability & Distribution: Concepts, Counting Rules, & Event Composition - Prof. Eun-Joo , Study notes of Probability and Statistics

The key concepts of probability and probability distribution from chapter 4 of ma 120. It covers the definition of probability, useful counting rules, and event composition and relations. Examples and formulas for calculating probabilities and the number of ways to arrange or choose events.

Typology: Study notes

Pre 2010

Uploaded on 08/04/2009

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MA 120
E. Lee
Summary(4.1-4.5)
Chapter 4 - Probability and Probability distribution
1. Probability = chance
experiment, event, simple event(an event that cannot be decomposed), sample space,
probability
Example 1) When tossing a die once, what is the probability to get odd number(s)?
experiment: toss a die and observe the number that appears on the upper face
event: observe an odd number = {1,3,5}
sample space(S) = the set of all simple events={1,2,3,4,5,6}
probability of the event = numbers in the event
numbers in the sample space =3
6=1
2
Note:
(a) Each probability must lie between 0 and 1.
(b) Probability of the sample space = P(S) = 1
2. Useful counting rules
(a) n! = n(n1)(n2) · · · (3)(2)(1) = n(n1)! = n(n1)(n2)!
Example 2) 3! = 6! = 0! = 1, 1! = 1
(b) Pn
r=n!
(nr)! (number of ways we can arrange rout of n)
Example 3) P3
2=3!
(3 2)! =(3)(2)(1)
1! = 6, P3
3=
(c) Cn
r=n!
r!(nr)! (number of ways we can choose rout of n)
Example 4) C3
2=3!
2!(3 2)! =(3)(2)(1)
(2)(1)(1) = 3, C8
3=
pf2

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MA 120

E. Lee

Summary(4.1-4.5)

Chapter 4 - Probability and Probability distribution

  1. Probability = chance experiment, event, simple event(an event that cannot be decomposed), sample space, probability

Example 1) When tossing a die once, what is the probability to get odd number(s)?

experiment: toss a die and observe the number that appears on the upper face event: observe an odd number = {1,3,5} sample space(S) = the set of all simple events={1,2,3,4,5,6} probability of the event = numbers in the event numbers in the sample space

Note: (a) Each probability must lie between 0 and 1. (b) Probability of the sample space = P (S) = 1

  1. Useful counting rules (a) n! = n(n − 1)(n − 2) · · · (3)(2)(1) = n(n − 1)! = n(n − 1)(n − 2)! Example 2) 3! = 6! = 0! = 1, 1! = 1

(b) P (^) rn = n! (n − r)! (number of ways we can arrange r out of n)

Example 3) P 23 =

= 6, P 33 =

(c) Crn = n! r!(n − r)! (number of ways we can choose r out of n)

Example 4) C 23 =

= 3, C 38 =

MA 120

E. Lee

Summary(4.1-4.5)

  1. Event composition and event relations (a) Ac^ = the complement of an event A consists of all the simple events in the sample space S that are not in A. P (A) + P (Ac) = 1

(b) A ∪ B

(c) A ∩ B

(d) P (A ∪ B)

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