Congratulations! You have just won the question-and-answer portion of a popular game show and will now be given an opportunity to select a grand prize. The game show host shows you a large revolving drum containing four identical white envelopes that have been thoroughly mixed in the drum. Each of the envelopes contains one of four checks made out for grand prizes of 24, 44, 64, and 84 thousand dollars. Usually, a contestant reaches into the drum, selects an envelope, and receives the grand prize in the envelope. Tonight, however, is a special night. You will be given the choice of either selecting one envelope or selecting two envelopes and receiving the average of the grand prizes in the two envelopes. If you select one envelope, the probability is 1/4 that you will receive any one of the individual grand prizes 24, 44, 64, and 84 thousand dollars. Assume you select two envelopes. There are six combinations, or samples, of two grand prizes that can be randomly selected from the four grand prizes 24, 44, 64, and 84 thousand dollars. The six samples are (24, 44), (24, 64), (24, 84), (44, 64), (44, 84), and (64, 84). What is the probability that you will receive a sample mean grand prize of at least 44 thousand dollars? (Enter the reduced fraction.)
Congratulations! You have just won the question-and-answer portion of a popular game show and will now be given an opportunity to select a grand prize. The game show host shows you a large revolving drum containing four identical white envelopes that have been thoroughly mixed in the drum. Each of the envelopes contains one of four checks made out for grand prizes of 24, 44, 64, and 84 thousand dollars. Usually, a contestant reaches into the drum, selects an envelope, and receives the grand prize in the envelope. Tonight, however, is a special night. You will be given the choice of either selecting one envelope or selecting two envelopes and receiving the average of the grand prizes in the two envelopes. If you select one envelope, the probability is 1/4 that you will receive any one of the individual grand prizes 24, 44, 64, and 84 thousand dollars. Assume you select two envelopes. There are six combinations, or samples, of two grand prizes that can be randomly selected from the four grand prizes 24, 44, 64, and 84 thousand dollars. The six samples are (24, 44), (24, 64), (24, 84), (44, 64), (44, 84), and (64, 84). What is the probability that you will receive a sample mean grand prize of at least 44 thousand dollars? (Enter the reduced fraction.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Ef 224.
Transcribed Image Text:Exercise 8.9 (Algo) THE GAME SHOW CASE
Congratulations! You have just won the question-and-answer portion of a popular game show and will now be given an opportunity to
select a grand prize. The game show host shows you a large revolving drum containing four identical white envelopes that have been
thoroughly mixed in the drum. Each of the envelopes contains one of four checks made out for grand prizes of 24, 44, 64, and 84
thousand dollars. Usually, a contestant reaches into the drum, selects an envelope, and receives the grand prize in the envelope.
Tonight, however, is a special night. You will be given the choice of either selecting one envelope or selecting two envelopes and
receiving the average of the grand prizes in the two envelopes. If you select one envelope, the probability is 1/4 that you will receive
any one of the individual grand prizes 24, 44, 64, and 84 thousand dollars.
Assume you select two envelopes. There are six combinations, or samples, of two grand prizes that can be randomly selected from
the four grand prizes 24, 44, 64, and 84 thousand dollars. The six samples are (24, 44), (24, 64), (24, 84), (44, 64), (44, 84), and (64, 84).
What is the probability that you will receive a sample mean grand prize of at least 44 thousand dollars? (Enter the reduced fraction.)
Probability
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