3. Each of the triples (ri, si , ti), i- 1...n, is a randomly chosen permutation of (1, 2, 3). Compute the three sums P, i-1 ri. P, i-1 si, and P, i=1 ti, and label them (not necessarily in order) A. B. C so that A S BS C. Let a, be the probability that A B-C and let b, be the probability that B = A +1 and C =B+1. Show that for every n 2 1. either 4a, s b, or 4a, +1 s b,+1.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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3. Each of the triples (ri, si, ti), i = 1...n, is a randomly chosen permutation of (1, 2, 3).
Compute the three sums P, i-1 ri, P, i-l si, and P, i=1 ti, and label them
(not necessarily in order) A. B. C so that A S B S C. Let a, be the
probability that A B-C and let b, be the probability that B = A +1 and
C = B+ 1. Show that for every n 2 1. either 4a, s b, or 4a, +1 s
b,+1.
Transcribed Image Text:3. Each of the triples (ri, si, ti), i = 1...n, is a randomly chosen permutation of (1, 2, 3). Compute the three sums P, i-1 ri, P, i-l si, and P, i=1 ti, and label them (not necessarily in order) A. B. C so that A S B S C. Let a, be the probability that A B-C and let b, be the probability that B = A +1 and C = B+ 1. Show that for every n 2 1. either 4a, s b, or 4a, +1 s b,+1.
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