Answered: The posterior probability of the…

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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Question

There is 0.3 probability that the time to complete a project will exceed the deadline. A forecast planning tool suggests that the deadline will be exceeded. In the past, the tool has given this forecast on 90% of occasions when the deadline has been exceeded and on 20% of occasions when it has not.
The posterior probability of the deadline being exceeded is:

1. 0.30

2. 0.66 (I think maybe this one?)

3. 0.41

A computer specialist estimates that there is a 0.8 probability that a computer failure has been caused by a fault in the computer’s motherboard. However, an electronic test which has a 90% probability of giving a correct indication and which can be assumed to be unbiased, indicates that the problem is not caused by the motherboard. The posterior probability that there is a fault in the motherboard is:

1. 0.31

2. 0.26 (I think maybe this one?)

A market research study will indicate that the sales of a new product in its first year will either be high, medium or low. Under which of these conditions would Bayes’s Theorem indicate that the prior probabilities should be revised, when the new information from the study is received?

1. when the prior probability of high sales is equal to 1.0

2. when it has the same probability of giving the three indications, irrespective of the actual sales level

3. when the prior probabilities are the same and the research has a 60% chance of correct indication (I think maybe this one?)

The prior probabilities that it will be fine or raining at 12.00 noon next Sunday when a parade is due to take place, are respectively 0.7 and 0.3. Two days before the parade, the local weather station will provide an unbiased forecast of either fine or rain. Given that its forecasts have a 90% probability of being correct, the probability that it will forecast fine weather:

1. 0.70 (I think maybe this one)

2. 0.66

3. 0.63

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