1. The CTA purple line runs express trains in the morning that go to the Loop, b
ID: 3051099 • Letter: 1
Question
1. The CTA purple line runs express trains in the morning that go to the Loop, bypassing many of the stops made by the red line on the same route. These trains arrive at the Davis stop at 15-minute intervals starting at 6 a.m. Red line trains arrive at the Davis stop at 15-minute intervals starting at 6:05 a.m. (a) If a certain passenger arrives at the Davis station at a time uniformly distributed between 6 and 7 a.m. and then gets on the first train that arrives, what is the probability that she boards the purple line express? (b) What if the passenger arrives at a time uniformly distributed between 6:10 and 8:10 a.m.?Explanation / Answer
a)as there is a gap of 10 minutes after red line depart and purple line to come whcih are 6:05 to 6:15 ; 6:20 to 6:30; 6:35 to 6:45 and 6:50 to 7:00
P(probability that boards the purple line =P(arrive between 6:05 to 6:15+arrive between 6:20 to 6:30+arrive between 6:35 to 6:45+arrive between 6:50 to 8:00)=(10+10+10+10)/60 =4/6 =2/3
b)P(probability that boards the purple line =P(arrive between 6:10 to 6:15+arrive between 6:20 to 6:30+arrive between 6:35 to 6:45+arrive between 6:50 to 8:00+arrive between 8:05 to 8:10) =(5+10+10+10+5)/60 =40/60
=2/3
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