Answer to Question #220264 in Statistics and Probability for Anshu

Question

Three boys go to the same school. Every boy needs two cubes of the same color to play a game, but the cubes that different boys have are not necessarily differently colored. A teacher has red, blue and green cubes in one drawer. If the teacher draws the cubes without looking, what is the least number of cubes that need to be pulled out to be sure that every boy can get two cubes of the same color?

Answer 1

Every boy has 2 Cubes out of 3 cubes. There are 6 possible ways

$$RR, BB, GG, RB, RG, BG$$

In first three cases boy already have two cubes of the same colour.

In remaining three cases there is a chance that one cube selected by teacher is of 3rd color.

But in 2nd draw cube will be one of the present three colors.

The least number of cubes that need to be pulled out to be sure that every boy can get two cubes of the same color is $3\cdot2=6.$