6. (1 Street, Brillantine Street, and Clancy Street. It is the beginning of rush

Question

6. (1 Street, Brillantine Street, and Clancy Street. It is the beginning of rush hour, and by experience Alabaster street will be closed by a car crash on average in 25 minutes, Brillantine street in 50 minutes, and Clancy Street in 40 minutes. Accident times are completely unpredictable. 0 pts.) There are 3 alternative routes by which you may drive to work: Alabaster If you leave for work in one hour (60 minutes), what is the probability that (at the moment you leave) a route to work will still be open?

Explanation / Answer

P(A) closed = 1 - e^(-60/25) = 0.909

P(B) closed = 1 - e^(-60/50) = 0.699

P(C) closed = 1 - e^(-60/40) = 0.777

P(at least one open) = 1 - P(all closed)

P = 1 - P(A) * P(B) * P(C)

P = 1 - 0.909 * 0.699 * 0.777

P = 0.506

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