Rolling Dice:

An employee at Data Reply chooses one die at random from a set of six k-sided dice: ={4, 6, 7, 8, 10, 20}. Each die is equally weighted and produces numbers from 1 to k. E.G. for k=6 (six sided die), the die produces numbers 1,2,3,4,5,6.

Given that one die chosen at random gives each of the following rolls (data): d=[5,2,7,4,2,6,7]

1. Given this data, what is the probability that it was the k-sided die (i.e. P(4-sided|d), P(6-sided | d), etc.)?

2. On average, how many rolls would it take until one could effectively rule out the 20sided die?

3. On average, how long would it take to roll three 1's in a row from a k-sided die.