Roads A, B, and C are the only way to escape from a certain provincial prison....

Roads A, B, and C are the only way to escape from a certain provincial prison. Prison records show that, of the prisoners who tried to escape, 9 % used road A, 14 % used road B, the remainder used road C. The records also indicate that 85 % of those who tried to escape using road A were captured. 13 % of those using road B were captured, and 58 % of those using road C were captured. Use four decimals in your answers (a) What is the probability that a prisoner escaping from this provincial prison is not captured? (b) What is the probability that a captured prisoner used road A in their escape attempt? (c) What is the probability that a prisoner who didn't get captured has used road C?

Solutions

Expert Solution

Probability that prisoner used road A to escape, P(A) = 0.09

Probability that prisoner used road B to escape, P(B) = 0.14

Probability that prisoner used road C to escape, P(C) = 1-0.09-0.14 = 0.77

Probability that prisoner who tried to escape using A were captured, P(Capture|A) = 0.85

Probability that prisoner who tried to escape using B were captured, P(Capture|B) = 0.13

Probability that prisoner who tried to escape using C were captured, P(Capture|C) = 0.58

a) Probability that prisoner is capture, P(Capture) =

Probability that prisoner is not capture, P(Not Capture) = 1 -P(Capture)

= 1- 0.5413 = 0.4587

b) Probability that captured prisoner used road A in their escape attempt, P(A|Capture) =

milcah answered 1 year ago

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