There are 90 applicants for a job with the news depart-ment of a television station. Some of them are college graduates and some are not; some of them have at leastthree years’ experience and some have not, with the exactbreakdown being CollegegraduatesNotcollegegraduatesAt least three years’ experience 18 9Less than three years’ experience 36 27If the order in which the applicants are interviewed bythe station manager is random, G is the event that thefirst applicant interviewed is a college graduate, and T isthe event that the first applicant interviewed has at leastthree years’ experience, determine each of the followingprobabilities directly from the entries and the row andcolumn totals of the table:(a) P(G); (b) P(T ); (c) P(G ∩T); (d) P(G ∩T ); (e) P(T|G); (f) P(G|T
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.
ment of a television station. Some of them are college
three years’ experience and some have not, with the exact
breakdown being
graduates
Not
college
graduates
At least three years’ experience 18 9
Less than three years’ experience 36 27
If the order in which the applicants are interviewed by
the station manager is random, G is the
first applicant interviewed is a college graduate, and T is
the event that the first applicant interviewed has at least
three years’ experience, determine each of the following
probabilities directly from the entries and the row and
column totals of the table:
(a) P(G); (b) P(T
|T
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