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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 83CR
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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.
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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