a) What is the probability that a customer chosen at random has been loyal 1 or more years given that he or she is from the Midwest? Round your answer to the nearest thousandth. b) What is the probability that a customer chosen at random is from the East given that he or she has been loyal from 10 to 14 years? Round your answer to the nearest thousandth. c) What is the probability that a customer chosen at random has been loyal from 3 to 4 years? Round your answer to the nearest thousandth.
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.
![a) What is the probability that a customer chosen at
random has been loyal 1 or more years given that he or
she is from the Midwest? Round your answer to the
nearest thousandth.
b) What is the probability that a customer chosen at
random is from the East given that he or she has been
loyal from 10 to 14 years? Round your answer to the
nearest thousandth.
c) What is the probability that a customer chosen at
random has been loyal from 3 to 4 years? Round your
answer to the nearest thousandth.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac1d06a1-aa98-45e4-8f95-fefe85883fe9%2Fec6852e8-599a-4401-bd95-e7d93c677168%2F0m98ey_processed.png&w=3840&q=75)
![Are customers more loyal in the East or in the West? The
following table is based on information from Trends in the
United Sates, published by the food marketing Institute,
Washington, D.C. The columns represent loyalty (in years)
at a primary supermarket. The rows represent regions of
the United States.
Less
15 or
Than 1- 2
3 - 4 5 - 9 10 - 14
Row
More
1
Years
Years Years| Years
Total
Years
Year
East
32
54
59
112
77
118
452
Midwest 31
68
68
120
63
173
523
South
53
92
93
158
106
158
660
West
41
56
67
78
45
86
373
Column
157
270
287
468
291
535
2008
Total](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac1d06a1-aa98-45e4-8f95-fefe85883fe9%2Fec6852e8-599a-4401-bd95-e7d93c677168%2F1wskdxq_processed.png&w=3840&q=75)
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