Question

You have an unbiased die, that is, a cube whose sides are labeled with numbers 1, 2, . . . , 6. When rolled, each of the numbers has equal probability of showing up on the top. How can you use the die to choose one of four elements uniformly at random? Briefly describe your method. What is the expected number of rolls in your method?

Answer 1

We will through the die two times and will se the sum of two. We know that if we through die two times then the possible number of outcomes are 36. So we can divide these 36 outcomes in 4 set of 9 outcomes. So we can say if the sum is 2 or 3 or 4 or 10 we will select element 1, if the sum is 4 or 5 we will select element 2, if sum is 8 or 9 we will select element 3, if sum is 7 or 11 or 12 we will select element 4.

In this way we can conclude that the expected number of throws will be 2.