Answer:
E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Step-by-step explanation:
Jessica is challenged to a game of sums.
Which means,
E(Dice 1) + E(Dice 2)
Let's first check the sum of all possible numbers of the two dice.
We have:
(1+1 = 2); (1+2=3); (1+3=4); (1+4+5); (1+5=6); (1+6=7); (2+1=3); (2+2=4); (2+3=5); (2+4=6); (2+5=7); (2+6=8); (3+1=4); (3+2=5); (3+3=6); (3+4=7); (3+5=8); (3+6=9); (4+1=5); (4+2=6); (4+3=7); (4+4=8); (4+5=9); (4+6=10); (5+1=6); (6+1=7); (6+2=8);*(6+3=9); (6+4=10); (6+5=11); (6+6+12);
Total possible outcome = 36 results.
(2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12)
Probability of even numbers =
E(even) =
Probability of odd numbers =
E(odd) =
Since they are equal,
E(even) = E(odd)
The correct choice for Jessica is:
E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.