Marvin is deciding a path from three (3) routes to reach = Village C (he is at Village A): A → Bk → C for k 1,2,3. He chooses the route A B C with probability Pk, where pi = : 0.4, p2 = 0.3, p3 = 0.3. B₁ A B2
Marvin is deciding a path from three (3) routes to reach = Village C (he is at Village A): A → Bk → C for k 1,2,3. He chooses the route A B C with probability Pk, where pi = : 0.4, p2 = 0.3, p3 = 0.3. B₁ A B2
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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Transcribed Image Text:Marvin is deciding a path from three (3) routes to reach
Village C (he is at Village A): A → B → C for k = 1,2,3. He chooses the route
A → Bk → C with probability Pk, where p₁ = 0.4, p2 = 0.3, p3 = 0.3.
k
B1
A
B₂
с
B3
The path connecting Bk → C may close, due to the seasonal construction, which
happens with probability qk (independent from Marvin's choice), where q₁ = 0.5, 92 = 0.6,
93 = 0.2. If the chosen route is not open, Marvin will return to Village A.
(a)
(b)
Find the probability that Marvin reaches Village C in one attempt.
Suppose Marvin reach Village C in one attempt. Find the probability
that he passes through B₂.
(c)
Let E be the event that Marvin reaches Village C in one attempt, and
F be that Marvin passes through Village B₂. Are these two events independent? Explain
your claim.
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