Question

You and your friend are rolling number cubes. Each cube has 6 sides with the numbers 1 to 6. If a sum of 7 is rolled, your friend gets 1 point. If a 2, 3, or 4 is rolled, you get 1 point. After 108 rolls each, what scores should you expect?

Friend: 54; You: 54

Friend: 18; You: 18

Friend: 54; You: 18

Friend: 18; You: 54

Answer 1

Friend: 18; you: 54
Because you have much bigger chance

Answer 2

Friend: 18; You: 54

Explanation:

You and your friend are rolling number cubes.

Each cube has 6 sides with the numbers 1 to 6.

Total Outcomes=36

{1,1};{1,2};{1,3}{1,4};{1,5};{1,6}

{2,1};{2,2};{2,3}{2,4};{2,5};{2,6}

{3,1};{3,2};{3,3}{3,4};{3,5};{3,6}

{4,1};{4,2};{4,3}{4,4};{4,5};{4,6}

{5,1};{5,2};{5,3}{5,4};{5,5};{5,6}

{6,1};{6,2};{6,3}{6,4};{6,5};{6,6}

If a sum of 7 is rolled, your friend gets 1 point.

Favorable outcomes for friend = {1,6};{2,5};{3,4};{4,3};{5,2};{6,1}=6

Total outcomes = 36

So, probability of getting a sum of 7 =
`(6)/(36)=(1)/(6)`

Since there are 108 rolls

So, expected score of friend =
`108 * (1)/(6)=18`

If a 2, 3, or 4 is rolled, you get 1 point.

So, probability of getting 2 =
`(1)/(6)`

So, probability of getting 3 =
`(1)/(6)`

So, probability of getting 4 =
`(1)/(6)`

So, So, probability of getting 2,3 or 4 =
`(1)/(6)+(1)/(6)+(1)/(6) =(3)/(6) =(1)/(2)`

So, your expected score =
`108 * (1)/(2)=54`

So, option D is correct.

Hence expected score of friend is 18 and yours expected score is 54