A police officer is using a radar device to check motorists’ speeds. Prior to beginning the speed check, theofficer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit.Assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selectedmotorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?(A) 0.0256(B) 0.1296(C) 0.3456(D) 0.8704(E) 0.9744
Question
A police officer is using a radar device to check motorists’ speeds. Prior to beginning the speed check, theofficer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit.Assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selectedmotorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?(A) 0.0256(B) 0.1296(C) 0.3456(D) 0.8704(E) 0.9744
Solution
The problem can be solved using the concept of binomial probability.
The probability of a single driver driving more than 5 miles per hour over the speed limit is 0.4 (40 percent).
The probability of a single driver not driving more than 5 miles per hour over the speed limit is 1 - 0.4 = 0.6.
We want to find the probability that at least 1 out of 4 drivers is driving over the speed limit. This is the same as 1 minus the probability that none of the 4 drivers are driving over the speed limit.
The probability that none of the 4 drivers are driving over the speed limit is (0.6)^4 = 0.1296.
So, the probability that at least 1 out of 4 drivers is driving over the speed limit is 1 - 0.1296 = 0.8704.
Therefore, the answer is (D) 0.8704.
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