Midterm1sol

# Midterm1sol - NAME: MAE 108 Probability and Statistical...

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NAME: MAE 108 – Probability and Statistical Methods for Engineers - Winter 2010 Midterm # 1 - January 29, 2010 50 minutes, open book, open notes, calculator allowed, no cell phones. Write your answers directly on the exam. 50 points total. (1) (10 points) A total of 28 percent of all roads in the US suﬀer from severe traﬃc jams, 7 percent are subject to very cold weather, and 5 percent are subject to both traﬃc jams and very cold weather. What percentage of rods in the US have neither traﬃc jams nor very cold weather? Solution: E = { the road has traﬃc jams } F = { the road has cold weather } A = { the road has neither traﬃc jams nor very cold weather } . We have A = ¯ E ¯ F so P ( A ) = P ( ¯ E ¯ F ) = 1 - P ( E F ) = 1 - P ( E ) - P ( F ) + P ( EF ) = 1 - 0 . 28 - 0 . 07 + 0 . 05 = 0 . 70.

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(2) (10 points) An insurance company believes that people who purchased insurance can be divided into two classes: those who are accident prone, and those who are not. Their statistics show that an accident-prone person will have an accident within a ﬁxed 1-year period with a probability of 40%, whereas this probability decreases to 20% for a non-accident-prone person. If we assume that 30 percent of the population is accident prone, what is the probability that a person will have an accident within a year of purchasing a policy? Solution:
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## This note was uploaded on 05/12/2010 for the course MAE 108 taught by Professor Lauga during the Winter '10 term at San Diego.

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Midterm1sol - NAME: MAE 108 Probability and Statistical...

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