Bill Borde, top advertising executive for Grapevine Concepts, has just launched a publicity campaign for a new restaurant in town, The Black Angus. Bill has just installed four billboards on a highway outside of town, and he knows from experience the probabilities that each will be noticed by a randomly chosen motorist. The probability of the first billboard’s being noticed by a motorist is 0.75. The probability of the second’s being noticed is 0.82, the third has a probability of 0.87 of being noticed, and the probability of the fourth sign’s being noticed is 0.9. Assuming that the event that a motorist notices any particular billboard is independent of whether or not he notices the others, what is the probability that (a) All four billboards will be noticed by a randomly chosen motorist? (b) The first and fourth, but not the second and third billboards will be noticed? (c) None of the billboards will be noticed? (d) The third and fourth billboards won’t be noticed?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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Bill Borde, top advertising executive for Grapevine Concepts, has just launched a publicity campaign for a new restaurant in town, The Black Angus. Bill has just installed four billboards on a highway outside of town, and he knows from experience the probabilities that each will be noticed by a randomly chosen motorist. The probability of the first billboard’s being noticed by a motorist is 0.75. The probability of the second’s being noticed is 0.82, the third has a probability of 0.87 of being noticed, and the probability of the fourth sign’s being noticed is 0.9. Assuming that the event that a motorist notices any particular billboard is independent of whether or not he notices the others, what is the probability that

(a) All four billboards will be noticed by a randomly chosen motorist?

(b) The first and fourth, but not the second and third billboards will be noticed?

(c) None of the billboards will be noticed?

(d) The third and fourth billboards won’t be noticed?

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