2.15 The highway system between cities A and B is shown in Fig. P2.I5. Travel be
ID: 3075179 • Letter: 2
Question
2.15 The highway system between cities A and B is shown in Fig. P2.I5. Travel between A and B during the winter months is not always possible because some parts of the highway may not be open to trafiic, because of extreme weather condition. Let E1, E2, E3 denote the events that highway AB, AC,and CB are open, respectively.
On any given day, assume
P(E1 = 2/5
P(E2) = 3/4
P(E3) = 2/3
p(E3 I E2) = 4/5
p(E1 l E2E3) = 1/2
(a) What is the probability that a traveter will be able to make a trip fromA to B if he has to pass through city c! Ans. 0.6.
(b) What is the probability that he will be able to get to city B? Ans. 0.7.
(c) Which route should he try first in order to maximize his chance of getting to B?
Figure P2.15Explanation / Answer
probability that a traveter will be able to make a trip fromA to B if he has to pass through city c
=P(E2 and E3 works)
=P(E2 n E3) =P(E2)*P(E3|E2) =(3/4)*(4/5)=3/5=0.6
b)
probability that he will be able to get to city B =P(E1)+P(E2 n E3)-P(E1 n E2 n E3)
=P(E1)+P(E2)*P(E3|E2)-P(E2)*P(E3|E2)*P(E1|E2 n E3)
=(2/5)+(3/4)*(4/5)-(3/4)*(4/5)*(1/2)=0.7
c)
one should select route E2 -E3; as it has higher probability 0.6 then E1 which is (2.5)=0.4.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.