Probability Question

[safirshahbaaz90]

Hi Tommy,

A bag contains 3 red, 4 white, and 5 blues marbles. Jason begins removing the marbles from the bag at random, one at a time. What is the least number of marbles he must remove to be sure that he has at least one of each colour?

A) 3
B) 6
C) 8
D) 10
E) 12

The answer is at the back is D(10). The reasoning given is that if Jason was really unlucky, then he would have to remove all 5 blue marbles, all 4 white marbles, and then a red. I, however thought the answer was A. If Jason was really lucky, then his first 3 marbles would be of different colours. Do we have to consider the worst case scenario for such questions?

Please help. :(

Thanks and Regards,
Safir

[tommywallach]

Hey Safir,

There's no such thing as "these types of questions." You simply have to pay attention to the language of the question. It asked "What is the least," which means we need to consider the ways in which he might not end up with one of each. If he got all blues and whites for the first 9 pulls, he would not yet have a red. So he'd have to pull that tenth to definitively have a red.

-t