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probability of her writing (+) is . Then, the slip is and D. Each of them either changes the sign on t leaves it as it is with probability - i. Compute the probability that the final sign is ( nuoh finol gian ig Clemp. nhilitu thot th

probability of her writing (+) is . Then, the slip is and D. Each of them either changes the sign on t leaves it as it is with probability - i. Compute the probability that the final sign is ( nuoh finol gian ig Clemp. nhilitu thot th

A First Course in Probability (10th Edition)
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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(a) A slip of paper is given to person A, who marks it with either (+) or (-). The probability of her writing (+) is . Then, the slip is passed sequentially to B,C, and D. Each of them either changes the sign on the slip with probability or leaves it as it is with probability i. Compute the probability that the final sign is (+) if A wrote (+). ii. Compute the probability that the final sign is (+) if A wrote (-). iii. Compute the probability that A wrote (+) if the final sign is (+). (b) There are n houses on a street numbered h1,..., hp. Each house can either be painted BLUE or RED. i. How many ways can the houses h1,..., h, be painted? ii. Suppose n > 4 and the houses are situated on n points on a circle. There is an additional constraint on painting the houses: exactly two houses need to be painted BLUE and they cannot be next to each other. How many ways can the houses h1, ..., h, be painted under this new constraint? iii. How will your answer to the previous question change if the houses are located on n points on a line.
Transcribed Image Text:(a) A slip of paper is given to person A, who marks it with either (+) or (-). The probability of her writing (+) is . Then, the slip is passed sequentially to B,C, and D. Each of them either changes the sign on the slip with probability or leaves it as it is with probability i. Compute the probability that the final sign is (+) if A wrote (+). ii. Compute the probability that the final sign is (+) if A wrote (-). iii. Compute the probability that A wrote (+) if the final sign is (+). (b) There are n houses on a street numbered h1,..., hp. Each house can either be painted BLUE or RED. i. How many ways can the houses h1,..., h, be painted? ii. Suppose n > 4 and the houses are situated on n points on a circle. There is an additional constraint on painting the houses: exactly two houses need to be painted BLUE and they cannot be next to each other. How many ways can the houses h1, ..., h, be painted under this new constraint? iii. How will your answer to the previous question change if the houses are located on n points on a line.
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