Statistics
Suppose that the probability is 1 in 3,900,000 that a single auto trip in the United States will result in the death of the driver. Over a lifetime, an average U.S. driver takes 50,000 trips. Assume that events are independent: (a) What is the probability of such a driver surviving 50,000 such trips? (b) What is the probability of having a fatal accident over the span of 50,000 trips? (c) Why might the assumption of independence be violated? (d) Why might a driver be tempted not to use a seat belt “just on this trip”?
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Answers
a) The probability of such a driver surviving 50,000 trips is roughly 0.997. b) The probability of having a fatal accident over the span of 50,000 trips is roughly 0.003. c) The assumption of independence might be violated because of factors such as the driver's age, level of intoxication, experience, cell phone usage, aggressiveness, or other external factors. d) A driver might be tempted not to use a seat belt “just on this trip” because they might feel that a seat belt will not make a difference on this trip or they may be in a rush and think that they don't have enough time to put it on.
