Question

A fair coin $1$ marked on one face and $6$ on the other and a fair are both tossed. Find the probability that the sum of numbers that turn up $3$ .

Answer 1

If the coin is tossed we get only $1$ or $6$

If a die is thrown we get $1,2,3,4,5,6$

Hence,

$S=\left\{\begin{array}{c}\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(1,5\right),\left(1,6\right),\\ \left(6,1\right),\left(6,2\right),\left(6,3\right),\left(6,4\right),\left(6,5\right),\left(6,6\right)\end{array}\right\}$

Then,

we get $n\left(S\right)=12$