Question

A fair six-sided die is tossed twice. What is the probability that a five will occur at least once?

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & (1,1) & (1,2)& (1,3)& (1,4)& (1,5)& (1,6)\\ \hdashline 2 & (2,1) & (2,2)& (2,3)& (2,4)& (2,5)& (2,6)\\ \hdashline 3 & (3,1) & (3,2)& (3,3)& (3,4)& (3,5)& (3,6)\\ \hdashline 4 & (4,1) & (4,2)& (4,3)& (4,4)& (4,5)& (4,6)\\ \hdashline 5 & (5,1) & (5,2)& (5,3)& (5,4)& (5,5)& (5,6)\\ \hdashline 6 & (6,1) & (6,2)& (6,3)& (6,4)& (6,5)& (6,6)\\ \hdashline \end{array}$$

$$P(5\ at\ least\ once)=\dfrac{11}{36}$$