\"If something can go wrong, it will go wrong.\" This funny saying is called Mur
ID: 3048729 • Letter: #
Question
"If something can go wrong, it will go wrong." This funny saying is called Murphy's law. Let's interpret this to mean "If something can go wrong, there is a very high probability that it will eventually go wrong."
Suppose we look at the event of having an automobile accident at some time during a day's commute. Let's assume that the probability of having an accident on a given day is 1 in a thousand or 0.001. That is, in your town, one of every thousand cars on a given day is involved in an accident (including little fender-benders). We also assume that having (or not having) an accident on a given day is independent of having (or not having) an accident on any other given day. Suppose you commute 42 weeks per year, 5 days a week, for a total of 210 days each year. In the following parts, write each probability in decimal form rounded to three places. (a) What is the probability that you have no accident over a year's time?
(b) What is the probability that you have at least one accident over a one-year period?
(c) Repeat part (a) for a 10-year period and for a 20-year period.
Repeat part (b) for a 10-year period and for a 20-year period.
?
10-year period ? 20-year period ?Explanation / Answer
Solution:
a) Probability of having an accident = 1/1000 = 0.001 = P
Probability of not having an accident = 1 - P = 0.999
Probability that you have no accident over a year = (P(no accident))^(210) [ since the events are given independent] = (0.999)^(210) = 0.8105
b) Probability that you have atleast one accident = 1 - P(having no accident)
=> 1 - Previous answer
=> 1 - 0.8104
=> 0.1896
c) For 10 year period
Probability that you have no accident over a 10 year = (P(no accident))^(2100) [ since the events are given independent] = (0.999)^(2100) = 0.1223
Probability that you have atleast one accident in 10 year = 1 - previous answer = 1 - 0.1223 = 0.8777
For 20 year period
Probability that you have no accident over a 20 year = (P(no accident))^(4200) [ since the events are given independent] = (0.999)^(4200) = 0.0149
Probability that you have atleast one accident in 10 year = 1 - previous answer = 1 - 0.0149 = 0.9851
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