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Exercise 1.7 A red pen and a green pen are put in a hat. A pen is chosen at random in the hat, and replaced inside after it color has been noted. • In case the pen is of red color, then a supplementary red pen is placed in the hat. . On the other hand if the pen color is green, then another green pen is added. After this first part of the experiment is completed, a second pen is chosen at random. Determine the probability that the first drawn pen was red, given that the color of the second pen chosen was red.

Exercise 1.7 A red pen and a green pen are put in a hat. A pen is chosen at random in the hat, and replaced inside after it color has been noted. • In case the pen is of red color, then a supplementary red pen is placed in the hat. . On the other hand if the pen color is green, then another green pen is added. After this first part of the experiment is completed, a second pen is chosen at random. Determine the probability that the first drawn pen was red, given that the color of the second pen chosen was red.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Exercise 1.7 A red pen and a green pen are put in a hat. A pen is chosen at random in the hat, and replaced inside after it color has been noted. • In case the pen is of red color, then a supplementary red pen is placed in the hat. • On the other hand if the pen color is green, then another green pen is added. After this first part of the experiment is completed, a second pen is chosen at random. Determine the probability that the first drawn pen was red, given that the color of the second pen chosen was red. Exercise 1.8 A machine relies on the functioning of three parts, each of which having a probability 1 - p of being under failure, and a probability p of functioning correctly. All three parts are functioning independently of the others, and the machine is working if and only if two at least of the parts are operating. (a) Compute the probability that the machine is functioning. (b) Suppose that the machine itself is set in a random environment in which the value of the probability p becomes random. Precisely we assume that p is a uniform random variable taking real values between 0 and 1, independently of the state of the system. Compute the probability that the machine operates in this random environment.
Transcribed Image Text:Exercise 1.7 A red pen and a green pen are put in a hat. A pen is chosen at random in the hat, and replaced inside after it color has been noted. • In case the pen is of red color, then a supplementary red pen is placed in the hat. • On the other hand if the pen color is green, then another green pen is added. After this first part of the experiment is completed, a second pen is chosen at random. Determine the probability that the first drawn pen was red, given that the color of the second pen chosen was red. Exercise 1.8 A machine relies on the functioning of three parts, each of which having a probability 1 - p of being under failure, and a probability p of functioning correctly. All three parts are functioning independently of the others, and the machine is working if and only if two at least of the parts are operating. (a) Compute the probability that the machine is functioning. (b) Suppose that the machine itself is set in a random environment in which the value of the probability p becomes random. Precisely we assume that p is a uniform random variable taking real values between 0 and 1, independently of the state of the system. Compute the probability that the machine operates in this random environment.
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