In a Special Report, "Speed Demons," in the Cedar Rapids

question 13

Essay

In a special report, "Speed Demons," in the Cedar Rapids, IA, Gazette, reporters used a radar gun to check the speeds of motorists in two counties. They were shocked (!) to discover that some motorists were driving at a speed greater than the posted limits. They reported the following information: Suppose that one of these cars is selected at random. Consider the following events: F = the event that a driver is in a "fast lane" (speed limit above 25 mph). S = the event that a driver is speeding. ​ ​ b) From the information in part (a), calculate .
c) From the information in part (a), calculate .
d) From the information in part (a), calculate P(S).
e) These events are represented in a tree diagram below. What is the probability that a randomly selected driver will "follow the branches" to the X?

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Definitions:

Expected Value

A calculated average outcome of a random variable, considering all possible outcomes and their probabilities.

Natural Log

A logarithm to the base e (where e is approximately 2.71828), used extensively in mathematical, economic, and scientific applications.

Risk Averter

An individual or entity that prefers to avoid uncertainty and potential losses when making investment or financial decisions.

Expected Value

In probability theory, it is the weighted average of all possible values of a random variable, with weights being the probabilities of each outcome.