To save on expenses, Rona and Jerry agreed to form a carpool for traveling to an
ID: 3225221 • Letter: T
Question
To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona prefers to use the somewhat longer but more consistent Queen City Avenue. Although Jerry prefers the quicker expressway, he agreed with Rona that they should take Queen City Avenue if the expressway has a traffic jam. The following payoff table provides the one-way time estimate in minutes for traveling to or from work:
Based on their experience with traffic problems, Rona and Jerry agreed on a 0.15 probability that the expressway would be jammed.
In addition, they agreed that weather seemed to affect the traffic conditions on the expressway. Let
C = clear
O = overcast
R = rain
The following conditional probabilities apply:
State of Nature Expressway Open Expressway Jammed Decision Alternative s1 s2 Queen City Avenue, d1 30 30 Expressway, d2 25 45 Weather Check No eather Check 0.695 c 0.2 150 0.09R 10 11 12 13 14 0.98 0.02 0.98 0.02 0.79 0.21 du 0.79 0.21 L 0.00 da 1.00 0.00 1.00 di 0.85 0.15 0.85 0.15 30 30 25 45 30 30 25 4 5 30 30 25 45 30 30 25 45Explanation / Answer
a)P(S1/C)=P(C/S1)*P(S1)/[P(C/S1)P(S1)+P(C/S2)P(S2)]
=(0.8*0.85)/(0.8*0.85+0.1*0.15)=0.978
P(S2/C)=P(C/S2)*P(S2)/[P(C/S1)P(S1)+P(C/S2)P(S2)]
=(0.1*0.15)/(0.8*0.85+0.1*0.15)=0.0216
P(S1/O)=P(O/S1)*P(S1)/[P(O/S1)P(S1)+P(O/S2)P(S2)]
=(0.2*0.85)/(0.2*0.85+0.3*0.15)=0.791
P(S2/O)=P(O/S2)*P(S2)/[P(O/S1)P(S1)+P(O/S2)P(S2)]
=(0.3*0.15)/(0.2*0.85+0.3*0.15)=0.209
P(S1/R)=P(R/S1)*P(S1)/[P(R/S1)P(S1)+P(R/S2)P(S2)]
=(0*0.85)/(0*0.85+0.6*0.15)=0
P(S2/R)=P(R/S2)*P(S2)/[P(R/S1)P(S1)+P(R/S2)P(S2)]
=0.6*0.15/(0*0.85+0.6*0.15)=1
b) tree iv) is the correct option
c)Expected travel time=0.695*(0.98*30+0.02*30+0.98*25+0.02*45)+0.215*(0.79*30+0.21*30+0.79*25+0.21*45)+0.09*(0+1*30+0+1*45)=57.98 minutes
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