Respuesta :
Answer:
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 =[tex]\frac{6}{36}=\frac{1}{6}[/tex]
Since there are 108 rolls
So, expected score of friend = [tex]108 \times \frac{1}{6}=18[/tex]
If a 2, 3, or 4 is rolled, you get 1 point.
So, probability of getting 2 = [tex]\frac{1}{6}[/tex]
So, probability of getting 3 = [tex]\frac{1}{6}[/tex]
So, probability of getting 4 = [tex]\frac{1}{6}[/tex]
So, So, probability of getting 2,3 or 4 = [tex]\frac{1}{6}+\frac{1}{6}+\frac{1}{6} =\frac{3}{6} =\frac{1}{2}[/tex]
So, your expected score = [tex]108 \times \frac{1}{2}=54[/tex]
So, option D is correct.
Hence expected score of friend is 18 and yours expected score is 54
