To avoid detection at customs, a traveler places
Lester John Sus
Answered question
2022-05-03
To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin pills that are similar in appearance. If the customs official selects 3 of the tablets at random for analysis, what is the probability that the traveler will be arrested for illegal possession of narcotics?
Answer & Explanation
karton
Expert2022-07-07Added 613 answers
A traveler places narcotic tablets in a bottle with 9 vitamin tablets that are similar in appearance (so, there will be total 6+9=15 tablets in the bottle).
The customs official selects 3 of the tablets at random for analysis.
* We need to find the probability that the traveler will be arrested for illegal possession of narcotics.
The traveler will be arrested if the customs official finds at least 1 narcotic table among 3 randomly selected tablets from the traveler's bottle.
Let random variable X represent the number of narcotic tablets among 3 randomly selected tablets from the traveler's bottle. Therefore, we need to find .
Lets consider as a success an event when the customs official finds the narcotic table.
So, we have a random sample of size n=3 (the custom official selects 3 tablets for
analysis), taken from items (there are 15 tables in the traveler's bottle) of which k=6 are labeled success (there are 6 narcotic tablets in the bottle) and are labeled failure.
Thus, X is hypergeometric random variable.
The probability distribution of hypergeometric random variable X is:
We need to find
According to probability distribution of the hypergeometric random variable X, we
have:
According equations (1) and (2), we get the required probability as follows:
So, the probability that the traveler will be arrested is 0.8154
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