Dealing with a weighted Dice:

Question

For this problem, assume that the outcomes 1 through 2 are equally likely, that the outcomes 3 through 6 are equally likely, and that outcome 1 is four times as likely as outcome 3.
(1) What probability should be assigned to rolling a 2?



(2) What probability should be assigned to rolling a 5?

Answer 1

Let p be the probability assigned to outcomes 1 and 2 and let q be the probability assigned to the outcomes 3,4,5,6.

 

One of the 6 outcomes must happen so 2p+4q = 1. Also, we are given p = 4q.

 

Now we solve.

 

2p + 4q = 1

 

2p + p = 1

 

3p = 1

 

p = 1/3

 

q = p/4 = 1/12

 

Thus there is a 1/12 chance that a 5 will be rolled.