Question

You have two dice: one has 2 threes, 2 fours, and 2 sixes, and the other has 5 ones and 1 five. You roll both dice. What is the expected value of the sum of the two faces?

A) 4.5

B) 3.8

C) 5

D) 6

E) 4

Answer 1

6

Explanation:

Let X be the number on first die and Y on second die

We have to calculate E(x+y)

=E(X)+E(Y)

X is a random variable taking values as

X 3 4 6

p 1/3 1/3 1/3

Hence E(x) =
`\Sigma x*p\\= (1)/(3) (4+5+6) =5`

Y is a random variable which takes values as

Y 1 5

p 5/6 1/6

E(Y) =
`\Sigma y*p\\= (1)/(6) (1+5) =1`

the expected value of the sum of the two faces

= 5+1 = 6