Ghi chú bài giảng về xác suất cơ bản và sự kiện môn Xác suất thống kê| Đại học Duy Tân

14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu Chapter 1: Basic Probability 1.1
Events, Sample Spaces and Probability
As experiment is an act of process of observation that leads to a single outcoe that cannot br predicted with certainty. A Head A Four An Ace
A sample point is the most basic outcome of an experiment.
A sample space of an experiment is the collection of all sample points. oRoll a single dice S:{1,2,3,4,5,6}
An event (biến cố) is a specific collection of sample point
oEvent A: Observe an even number. A={2,4,6}
Mutually exclusive events
oEvents that cannot occur together
Collectively exhaustive events oOne of the events must occur
oThe set of events covers the entire sample space Example A=aces; B=black cards C=diamonds; D=hearts
oEvents A,B,C and D are collectively exhaustive (but not mutually exclusive – an ace may also be a heart)
oEvents B,C and D are collectively exhaustive and also mutually exclusive
Probability (Xác suất)
Probability is the chance that some event may happen
It is the ratio of the number of ways a certain event can occur to the number of possible outcomes 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu
Probility is the numerical measure of the likehood that an event wil occur.
The probability of any event must be between 0 and 1, inclusively
0≤P (A )≤1forany event A 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu Assesing Probability
Thre are three approaches to assesing the probability of an uncertain event
1. The Classical Aproach
Probability yof occurrence=XT=number of theways theevent canoccur
totalnumber of elementaryoutcomes
2. The Relative Frequency Approach
Probability yof occurrence=numberof favorableoutcomes observed
totalnumber of outcomesobserved
3. The Subjectie Approach
An indvidual judgment or opinion about the probability of occurrence 1.2 Unions and Intersections Compound Events - Made of two or more than other events Union Intersection
The complement of any event A is the event that A does not occur, AC Example
A:{Tossanevent number }
AC:{Tossanodd number } 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu 1.3 Complementary Events A+B=A∪B
A.B=AB=A∩B 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu
(A+B)C=AC.BC
P (A )+P (AC )=1
P (A )=1−P (AC )
P (AC )=1−P(A) 1.4 General Addition Rule General Addition Rule: A+B=A∪B
A.B=AB=A∩B
P (A∪B )=P (A )+P (B)−P (A∩ B )
P (A+B )=P (A )+P (B)−P (AB )
If A and B are mutually exclusive, then p9aP (A∩B )=P (A )+P (B)=0, so the rule can be simpliified:
For mutually exclusive events A and B
P (A∪B )=P (A )+P (B) 1.5 Conditional Probability
A conditional probability is the probability of one event, given that another event has occurred =P(A∧B) P (A|B ) P(B)
=> The conditional probabilty of A =P(A∧B) P (B|A ) P(A)
When P (A∧B )=jointprobability (xác suất liên kết)
P (A )=marginalprobability (xác suất biên)
P (B)=marginalprobability (xác suất biên) 1.6 The Multiplicative Rule
Events A and B are independent when the probability of one event is not affected by the other event.
Multiplication rule of two events A and B 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu p
P (A∩B )=P (B )P (A|B)=P (A )P(B |A) The conditional probabl 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu P (event)=❑ ❑ 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu 14:19, 11/01/2026
TOAH201 - Ghi chú bài giảng về xác suất cơ bản và sự kiện - Studocu