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

Answer:

6

Step-by-step 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) = $\Sigma x*p\\= \frac{1}{3} (4+5+6) =5$

Y is a random variable which takes values as

Y   1     5

p   5/6  1/6

E(Y) = $\Sigma y*p\\= \frac{1}{6} (1+5) =1$

the expected value of the sum of the two faces

= 5+1 = 6