Suppose you have a non-standard 6-sided dice D. The sides of D are numbered as follows. Exactly three of the sides have the number 1, two of the sides have the number 2, and one of the sides has the number 3, with each side having exactly one number. Suppose that whenever you roll D, each of its 6 sides is equally likely to be the number you get. Thus, for example, every time you roll D the chance that you get the number 1 is 3 6 , since 3 of its sides are the number 1. Suppose you roll D 10 times.
a) What is the probability that you got the same number on all 10 rolls?
b) What is the probability that you got the same number on at least 9 of your 10 rolls? For example, (1,2,1,1,1,1,1,1,1,1) would count here, since you got the same number on 9 of your 10 rolls. (2,2,2,2,2,2,2,2,2,2) would also count here, since you got the same number on all 10 of your rolls