Question 1126252: "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 46 weeks per year, 5 days a week, for a total of 230 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 30-year period.
10-year period
30-year period
Repeat part (b) for a 10-year period and for a 30-year period.
10-year period
30-year period
(d) Does your work support the idea that there is a mathematical basis for Murphy's law as we interpreted it?
Yes, even though the possibility of a crash is slim, the probability of an event over a long period of time is large.
Yes, the possibility of a crash is large and the probability of an event over a long period of time is large.
No, even though the possibility of a crash is large, the probability of an event over a long period of time is slim.
No, the possibility of a crash is slim and the probability of an event over a long period of time is sli
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! probability of no accident on a given day is 0.999
For a year of 230 days, that probability of no accident is 0.999^230=0.7944
For 10 years, it would be 0.1001
For 30 years, it would be 0.0010
At least one accident has a probability of 1-prob(no accident) or 0.2056 year1
For 10 years,it would be 0.8999
For 30 years, it would be 0.9990
The first part is closest--low probability events that over a long period of time have an expected value > 0 will eventually happen. Expected value here is probability * time
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