Question

How to find the probability using discrete variables?

Can someone please explain to me how to do question 11? Thanks!

Answer 1

First of all please note that it is a four sided, unbiased die and that means when you throw the die the probability of getting 1, 2 , 3 or 4 on the face in the contact with table will be equal to 1/4.
In order to find the probability of the score X, you have to go through the following steps

1) List all the possible outcomes of throwing two dice which are form of a regular tetrahedron
So we will have
(1,1) (2,2) (3,3) (4,4)
(1,2) (2,1) (3,1) (4,1)
(1,3) (2,3) (3,2) (4,2)
(1,4) (2,4) (3,4) (4,4)
For this case we have 16 possible outcomes

2) Based on the observation above, now we can find the probability distribution of X.

x 1 I 2 I 3 I 4 I 6 I 8 I 9 I 12 I16

P(x=X)1/16 I 2/16 I 2/16 I 3/16 I 2/16 I 2/16 I 1/16 I 2/16 I

1/16

You can create a table with the values above, that would give you a better understanding of the probability distribution.

Determine the values of:

P(X>8) = P(X=9) + P(X=12) + P(X=16)

          = 1/16 + 2/16 + 1/16

          = 4/16

           = 1/4

Both E(X) and Var(X) can be found easily through referring the previous steps.