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

Friend: 18; You: 54

Step-by-step 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 =

Since there are 108 rolls

So, expected score of friend =

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

So, probability of getting 2 =

So, probability of getting 3 =

So, probability of getting 4 =

So, So, probability of getting 2,3 or 4 =

So, your expected score =

So, option D is correct.

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

the median here is 25. your lowest value is 14 and highest value is 48. to find the third quartile, find the medium number in between 25 and 48 which would be 42 i believe.