If subjective probabilities are determined by themethod suggested in Exercise 16, the third postulate ofprobability may not be satisfied. However, proponentsof the subjective probability concept usually impose thispostulate as a consistency criterion; in other words, they regard subjective probabilities that do not satisfy the pos-tulate as inconsistent. (a) A high school principal feels that the odds are 7 to 5against her getting a $1,000 raise and 11 to 1 against hergetting a $2,000 raise. Furthermore, she feels that it is aneven-money bet that she will get one of these raises orthe other. Discuss the consistency of the correspondingsubjective probabilities.(b) Asked about his political future, a party officialreplies that the odds are 2 to 1 that he will not run forthe House of Representatives and 4 to 1 that he will notrun for the Senate. Furthermore, he feels that the oddsare 7 to 5 that he will run for one or the other. Are thecorresponding probabilities consistent?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
method suggested in Exercise 16, the third postulate of
probability may not be satisfied. However, proponents
of the subjective probability concept usually impose this
postulate as a consistency criterion; in other words, they
tulate as inconsistent.
against her getting a $1,000 raise and 11 to 1 against her
getting a $2,000 raise. Furthermore, she feels that it is an
even-money bet that she will get one of these raises or
the other. Discuss the consistency of the corresponding
subjective probabilities.
(b) Asked about his political future, a party official
replies that the odds are 2 to 1 that he will not run for
the House of Representatives and 4 to 1 that he will not
run for the Senate. Furthermore, he feels that the odds
are 7 to 5 that he will run for one or the other. Are the
corresponding probabilities consistent?
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