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2. The probability that both will catch the bus within 15 minutes, given they are still waiting after 10 min- utes;

2. The probability that both will catch the bus within 15 minutes, given they are still waiting after 10 min- utes;

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...
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Ugo and Vittorio arrive at the bus stop and wait for two different buses. Let U and V be the waiting time until they catch the bus of Ugo and Vittorio, respectively. Assume the time to be independent and exponentially distributed with mean 15. Compute: 1. The probability that both will catch the bus within 15 minutes; 2. The probability that both will catch the bus within 15 minutes, given they are still waiting after 10 min- utes; 3. The probability that Vittorio waited less than 5 minutes, given he is not at the bus stop after 15 minutes; 4. The probability that Vittorio will wait at least 10 minutes less than Ugo.
Transcribed Image Text:Ugo and Vittorio arrive at the bus stop and wait for two different buses. Let U and V be the waiting time until they catch the bus of Ugo and Vittorio, respectively. Assume the time to be independent and exponentially distributed with mean 15. Compute: 1. The probability that both will catch the bus within 15 minutes; 2. The probability that both will catch the bus within 15 minutes, given they are still waiting after 10 min- utes; 3. The probability that Vittorio waited less than 5 minutes, given he is not at the bus stop after 15 minutes; 4. The probability that Vittorio will wait at least 10 minutes less than Ugo.
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