Question

Archie rolls two number cubes, each with sides numbered 1 through 6. He finds the sum of the numbers on the tops of the cubes. Whaf two sums have the probability?

A. 3 and 4
B. 5 and 9
C. 5 and 8
D. 10 and 12

Answer 1

The same probability*

Write firstly what results it's able to get and their sum:
.....1....2.....3.....4....5.....6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

As you can see there are four options to get "5" and also four options to get "9".
So the B is proper answer.
Sum 5 and sum 9 have the same probability.

Answer 2

`\Omega=\{(x;y):x;y\in\{1;\ 2;\ 3;\ 4;\ 5;\ 6\}\}\\\\\overline{\overline{\Omega}}=6^2=36\\\\A=\{(1;2);\ (2;1);\ (1;3);\ (3;1);\ (2;\ 2)\};\ \overline{\overline{A}}=5;\ P(A)=(5)/(36)\\\\B=\{(1;4);\ (4;1);\ (2;3);\ (3;2);\ (3;6);\ (6;3);\ (4;5);\ (5;4)\};\\\overline{\overline{B}}=8;\ P(B)=(8)/(36)\\\\C=\{(1;4);\ (4;1);\ (2;3);\ (3;2);\ (2;6);\ (6;2);\ (3;5);\ (5;3);\ (4;4)\}\\\overline{\overline{C}}=9;\ P(C)=(9)/(36)`


`D=\{(4;6);\ (4;6);\ (5;5);\ (6;6)\};\ \overline{\overline{D}}=4;\ P(D)=(4)/(36)`




`A.\\3\to(1;2);\ (2;1)\to(2)/(36)\\4\to(1;3);\ (3;1);\ (2;2)\to(3)/(36)\\\\B.\\5\to(1;4);\ (4;1);\ (2;3);\ (3;2)\to(4)/(36)\\9\to(3;6);\ (6;3);\ (4;5);\ (5;4)\to(4)/(36)`


`C.\\5\to(1;4);\ (4;1);\ (2;3);\ (3;2)\to(4)/(36)\\8\to(2;6);\ (6;2);\ (3;5);\ (5;3);\ (4;4)\to(5)/(36)\\\\D.\\10\to(4;6);\ (6;4);\ (5;5)\to(3)/(36)\\12\to(6;6)\to(1)/(36)`