Module 4 Basic Probability Flashcards
To understand basic probability concepts & conditional probability.
The ______ _____ is the collection of all possible outcomes of a variable
e.g., all 6 faces of a die
e.g., Two sides of the same coin
Sample space
*An event described by a single characteristic.
*E.g., A day in January from all days in 2019
Simple Event
*An event described by two or more characteristics.
*E.g., A day in January that is also a Wednesday from all days in 2019.
Joint Event
*All events that are not part of event A
*E.g., All days from 2019 that are not in January
Complement of an even A (denoted A’)
-The numerical value representing the chance, likelihood, or possibility that an event will occur (Always between 0 and 1).
Probability
-An event that has no chance of occurring (probability = 0)
Impossible Event
-An event that is sure to occur (probability = 1)
Certain Event
*Events that cannot occur simultaneously
Ex: Tuesday & Wednesday
Mutually exclusive events
*One of the events must occur.
*The set of events covers the entire sample space.
EX: Randomly choose a day from 2019
-A = Weekday;
-B =Weekend
Collectively Exhaustive Events
When randomly selecting a day from the year 2019 what is the probability the day is in January?
X/T = 31 (days in Jan.)/365 (days in a year)
Probability of occurence
*___________ is the numerical measure of the likelihood that an event will occur.
*the ___________ of any event must be between 0 and 1, inclusively.
*The sum of the _____________ of all mutually exclusive and collectively exhaustive events is
Probability
0 ≤ P(A) ≤1 For any event A
Probability
P(A)+P(B) +P(C)=1
-If A,B, and C are mutually exclusive and collectively exhaustive
Probability
Summarizing Sample spaces
Contingency Table
Summarizing Sample spaces
Venn Diagram
*______ (=marginal) Probability refers to the probability of a simple event
-P(Planned to purchase)
-P(Actually purchased)
Simple
_____ Probability refers to the possibility of an occurrence of two or more events
-ex. P(Plan to Purchase and Purchase).
-ex. P(No Plan and Purchase).
Joint Probability
(Exercise:) What is the probability of “bought TV”?
Simple Probability
(Exercise:) What is the probability of “planned to buy TV” and “bought TV”?
Joint Probability
P(A or B) = P(A) + P(B) - P(A and B)
P(A U B)=P (A) + P(B) - P(A ∩ B)
General Additional Rule
If A and B are ________ exclusive, then P(A and B) = 0, so the rule can be simplified:
P(A or B) = P(A) + P(B)
P(A U B) = P (A) + P(B)
mutually exclusive
What is the Probability of “planned to buy TV” or “bought TV?
Actually bought | did not | Total
Bought | 200 | 50 | 250
Did not buy | 100 | 650 | 750
Total | 300 | 700 | 1,000
P(A U B) = P(A) + P(B) - P(A ∩ B)
250/1,000+ 300/1,000 - 200/1,000 = 350/1,000 = 0.35 (35%)
-A ___________ probability is the probability of one event, given that another event has occurred
conditional probability
P(A | B) = P(A and B)/P(B)
The conditional probability of A given that B has occurred.
P(B | A) P(A and B)/P(A)
The conditional probability of B given that A has occurred.
P(A and B) =
Joint probability of A and B
P(A) =
marginal or simple probability of A
P(B) =
Marginal or simple probability of B
-Two events are independent if and only if:
P(A|B)=P(A)
P(A|B)=P(A)
*Events A and B are independent when the probability of one event is not affected by the fact that the other event has occurred.
