To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle

Question

To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets 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? A nationwide survey of college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in Parade. If 12 seniors are selected at random and asked their opinion, find the probability that the number who disapprove of smoking pot daily is anywhere from 7 to 9; at most 5; not less than 8.

Explanation / Answer

1) WE HAVE 6 NARCOTICS TABLETS AND 9 VITAMINS TABLETS

THEREFORE TOTAL WE HAVE 15 TABLETS

NOW THE PROBABILITY OF GETTING NARCOTICS TABLETS = 6/15 = 0.4

PROBABILITY OF NOT GETTING NARCOTICS TABLETS = 1 - 0.4 = 0.6

NOW N = 3

THE PERSON WILL BE ARRESTED EVEN IF 1 TABLET OF NARCOTICS IS TAKEN OUT

NOW WE NEED TO DINF THE PROBABILITY THAT ATLEAST 1 NARCOTICS TABLET IS SELECTED

PROBABILITY( ATLEAST ONE NARCOTICS TABLET) = 1 - PROBABILITY(0 NARCOTICS TABLETS)

P(0 NARCOTICS TABLET SELECTED = 3C0*(0.4)^0*(0.6)^3 = 0.216

THEREFORE PROBABILITY(AT LEAST ONE) = 1-0.216 = 0.784

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