In a Prince Market Research Survey of 2518 motorists, 252 said they made an obsc
ID: 3260923 • Letter: I
Question
In a Prince Market Research Survey of 2518 motorists, 252 said they made an obscene gesture in the previous month.
A) If 2 of the surveyed motorists are randomly selected with replacement, what is the probability that each of them made an obscene gesture?
B) If 2 of the surveyed motorists are randomly selected without replacement, what is the probability that each of them made an obscene gesture?
C) If 2 of the surveyed motorists are randomly selected with replacement, what is the probability that each of them did not make an obscene gesture?
D) If 2 of the surveyed motorists are randomly selected without replacement, what is the probability that each of them did not make an obscene gesture?
Explanation / Answer
Probability that a selected motorist made an obscene gesture in the previous month = 252 / 2518 = 0.1.
A) If of the surveyed motorists are randomly selected with replacement, the probability that each of them made an obscene gesture = (0.1 * 0.1) = 0.01. (Ans).
B) If 2 of the surveyed motorists are randomly selected without replacement, the probability that first selected motorist made an obscene gesture = 0.1.
The probability that second selected motorist made an obscene gesture = 251 / 2518 = 0.09968.
Hence the probability that each of them made an obscene gesture = 0.1 * 0.0997 = 0.009968. (Ans).
C) The probability that a randomly selected motorist didn't make an obscene gesture = 1 - 0.01 = 0.99.
If 2 of the surveyed motorists are randomly selected with replacement, the probability that each of them did not make an obscene gesture = 0.99 * 0.99 = 0.9801. (Ans).
D) If 2 of the surveyed motorists are randomly selected without replacement, the probability that first selected motorist did not make an obscene gesture = 0.99.
The probability that second selected motorist did not make an obscene gesture = 1- (252 / 2517) = 0.89988
Hence the probability that each of them did not make an obscene gesture = (0.99 * 0.89988) = 0.89088. (Ans).
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