Question

Suppose that a single die with 7 sides (numbered 1, 2, 3, ... , 7) is rolled twice. what is the probability that the sum of the two rolls equals 6 ?

Answer 1

$\Omega=\{(1;1);\ (1;2);\ (1;3);\ ...;\ (7;6);\ (7;7)\}\\\\|\Omega|=7^2=49$

$A=\{(1;\ 5);\ (2;\ 4);\ (3; 3);\ (4;\ 2);\ (5;\ 1)\}\\\\|A|=5$

$\boxed{P(A)=\dfrac{5}{49}}$