Random event
Simple event
Composite event
Ask two people if interest rates are going up
They must answer “yes” or “no”
Simple events: a1 = (Y,Y), a2 = (Y,N),
How Random Events Relate
Complementary events
Two random event for which all basic outcomes not contained in one event are
A
contained in the other event (denoted A and , the bar denoting ‘complementary’)
Such events are both mutually exclusive and collectively exhaustive at the same
time
Unions of Events (logical operator U [or])
All basic outcomes contained in one or the other event
∩
Intersections of Events (logical operator [and])
All basic outcomes contained in one and the other event
Probability Concepts
Objective Probability: The theoretical Approach
Relies entirely on abstract reasoning
Logic provides all answers
The probability of an event A:
p(A)= n
N Here, n is the number of equally likely basic outcomes that are favorable to the
occurrence of event A, while N is the total number of equally likely basic outcomes
possible
Example (Objective Probability)
An unbiased die has 6 faces ({1,2,3,4,5,6}), each equally likely. Hence the theoretical
probability of obtaining the face ‘1’ in one toss of the die is 1/6 = 0.166667
Objective Probability: The Empirical Approach
Probability values are derived from dta, i.e. experience
The probability of an event is equal to the relative frequency with which it has
actually been observed in the past
The probability of an event A:
k
p(A)= M
Here, k is the number of times A occurred in the past during a large number of random
experiments, while M is the maximum number of times A could have occurred
Example
Roll a die, say, M = 60,000 times and record each outcome. If there were
An alternative to objectively obtained probabilities can be found in the notion ‘subjective
probability’
Subjective Probability
Purely personal beliefs in the degree of likelihood that some event will occur
Hunches people have, e.g.,
The likelihood of a recession this year
The likelihood of oil being found at a given site
Counting Techniques
Factorials: Let n be a positive integer. The product of all integers from 1 to n is called ‘n
factorial’, and is denoted as n! = n x ( n -1) x (n-2) x

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