You are playing a game that involves rolling** two fair dice** (number cubes) numbered 1 through 6.

If the score for one roll of the game is the **sum **of the two numbers on the dice, what are the smallest and largest possible outcomes? What is the **expected value** for the outcome? What is the** value and the probability **the most likely outcome? **Show your work! **

Thanks so much for your help.

Guest May 20, 2018

#1**0 **

The smallest outcome is: 1 + 1 =** 2**

The largest outcome is: 6 + 6 =** 12**

The expected value: [1+2+3+4+5+6] x 2 / 6 =** 7**

The value of the most likely outcome is** 7 **as above:

The probability of getting a 7 is: [1+6, 2+5, 3+4, 4+3, 5+2, 6+1] =6 outcomes / 6^2 = 6/36 =**1/6**

Guest May 20, 2018

#2**+2 **

1. All we need to do is find the expected value for one die, then do what the problem asks us to do.

The expected value for the first die was:

\(\frac{1+2+3+4+5+6}{6}=3.5\),

\(3.5+3.5=\boxed7\),

That is the expected value for the outcome.

2.

The probabilty of getting a sum of 2 is: \(\frac{1}{36}\). The numerator is one, because there is one way of getting a sum of 2, 1 + 1.

We do the same for the rest of the sums,

The probabilty of getting a sum of 3 is: \(\frac{2}{36}\), (1,2) ; (2,1)

The probabilty of getting a sum of 4 is: \(\frac{3}{36}\), (1,3) ; (3,1) ; (2,2)

The probabilty of getting a sum of 5 is: \(\frac{4}{36}\), (1,4) ; (4,1) ; (2,3) ; (3,2)

The probabilty of getting a sum of 6 is: \(\frac{5}{36}\), (1,5) ; (5,1) ; (2,4) ; (4,2) ; (3,3)

The probabilty of getting a sum of 7 is: \(\frac{6}{36}\), (1,6) ; (6,1) ; (2,5) ; (5,2) ; (3,4) ; (4,3)

The probabilty of getting a sum of 8 is: \(\frac{5}{36}\), (2,6) ; (6,2) ; (3,5) ; (5,3) ; (4,4)

The probabilty of getting a sum of 9 is: \(\frac{4}{36}\), (3,6) ; (6,3) ; (4,5) ; (5,4)

The probabilty of getting a sum of 10 is: \(\frac{3}{36}\), (4,6) ; (6,4) ; (5,5)

The probabilty of getting a sum of 11 is: \(\frac{2}{36}\), (5,6) ; (6,5)

The probabilty of getting a sum of 12 is: \(\frac{1}{36}\), (6,6)

The most likely outcome is getting a 7, with a 1/6 probability.

3.

Greatest is 6 + 6 = 12

Smallest is 1 + 1 = 2

GYanggg May 20, 2018