5. A decision maker subjectively assigned the following probabilities to the all the four possible outcomes of an activity: P(E1) = 0.35, P(E2) = 0.12, P(E3) = 0.44, and P(E4) = 0.20. (a) Are these probability assignments valid? Yes or No. (b) Give reason for your answer in 5(a).

5. A decision maker subjectively assigned the following probabilities to the all the four possible outcomes of an activity: P(E1) = 0.35, P(E2) = 0.12, P(E3) = 0.44, and P(E4) = 0.20. (a) Are these probability assignments valid? Yes or No. (b) Give reason for your answer in 5(a).

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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An experiment consists of two independent trials. The outcomes of the first trial are A, B, and C, with probabilities of occurring equal to 0.2, 0.4, and 0.4, respectively. The outcomes of the second trial are E and F, with probabilities of occurring equal to 0.7 and 0.3. Draw a tree diagram representing this experiment. Use this tree diagram to find the probabilities below. (a) P(B)(b) P(F | B)(c) P(B F)(d) P(F)(e) Does P(B F) = P(B) · P(F)? YesNo (f) Are B and F independent events? YesNo
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.91, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to six decimal places.
A geologist has collected 19 specimens of basaltic rock and 19 specimens of granite. The geologist instructs a laboratory assistant to randomly select 33 of the specimens for analysis. (a) What is the pmf of the number of granite specimens selected for analysis? (Round your probabilities to four decimal places.) P(x) (b) What is the probability that all specimens of one of the two types of rock are selected for analysis? (Round your answer to four decimal places.) (c) What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value? (Round your answer to four decimal places.)
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