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?

The probability is 0.3, or 30%.

These are not independent events; one pill being chosen will affect the probability after that, as the pill will not be replaced before selecting the next one.

The probability of getting exactly 1 narcotic pill is given by:
(6/15)(9/14)(8/13) = 432/2730.  It does not matter what order the narcotic pill is in, the overall product will be the same.

The probability of getting exactly 2 narcotic pills is given by:
(6/15)(5/14)(9/13) = 270/2730.  Again, the order these are found in does not matter, as it is multiplication and will not change the product.

The probability of all 3 pills being narcotics is given by:
(6/15)(5/14)(4/13) = 120/2730.

Adding these three possibilities together, we have 822/2730 = 0.30.