Answer Choices: 1/64 7/64 3/16 13/64

Question

In a game a player is a biased tetrahedron for faced die. The probability of each possible scores shown below find the probability of a total score of six after two rolls. 

Score: 1 , 2 , 3 , 4 

Probability: 1/4 , 1/4 , 1/8 , x

Answer 1

First let's solve for x. The probabilities must sum to 1 for it to be a valid probability distribution, so 1/4 + 1/4 + 1/8 + x = 1. So x = 3/8.

There are 3 ways to get a score of 6 after 2 rolls:

1. (2,4)
2. (4,2)
3. (3,3)

We can find the probability of each of these outcomes by multiplying together the probabilities of the individual rolls, because they are independent events.

1. (2,4): 1/4 * 3/8 = 3/32
2. (4,2): 3/8 * 1/4 = 3/32
3. (3,3): 1/8 * 1/8 = 1/64

Each of these series of two rolls are disjoint events, so we can add them together to find the probability that any of them happen. The probability of a score of 6 after 2 rolls is 3/32 + 3/32 + 1/64 = 13/64.