Question

The most commonly used dice are six-sided, with numbers 1 through 6 on the faces. Tom is playing a game in which he is rolling two six-sided dice. In the game, then, the smallest possible sum on the two dice is 2, and the largest possible sum is 12.

(a) What is the expected value of the sum of the two dice?

(b) What is the probability of rolling a sum of 8?

(c) What is the probability of rolling a sum of 12?

(d) What is the probability of rolling a sum smaller than 13?

(e) What is the probability of rolling a sum of 3 or 11?

Answer 1

Explanation:

Given that Tom is playing a game in which he is rolling two six-sided dice.

The outcomes are 36, and sample space would be

(1,1) (1,2)...(1,6), (2,1),,,,,, (6,3)...(6,6)

a) The sum X can take values as

X 2 3 4 5 6 7 8 9 10 11 12

p 1/36 1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36 1

xp 1/18 1/6 1/3 5/9 5/6 1 1/6 1 1/9 1 5/6 11/18 1/3 7

So E(x) = 7

b) P(X=8) =
`(1)/(9)`

c)
`P(x=12) = (1)/(36)`

d) P(X<13) = 1 (certain event)

e)
`P(3 or 11) = P(3)+P(11)\\=(2)/(18) \\=(1)/(9)`