A pair of dice is thrown. Then the probability that either of the dice shows 2 when their sum is 6 is
A pair of dice is thrown. Then the probability that either of the dice shows 2 when their sum is 6 is
$\frac{1}{2}$
$\frac{1}{5}$
$\frac{2}{5}$
$\frac{3}{5}$
Solution
Let $E_1=$ Either of dice shows 2
$E_2=$ Sum of pair is 6 .
Then, $E_2=\{(1,5)(2,4),(4,2),(3,3)(5,1)\}$ and $E_1=\{(2,4)(4,2)\}$
$P\left(\frac{E_1}{E_2}\right)=\frac{P\left(E_1 \cap E_2\right)}{P\left(E_2\right)}=\frac{2 / 36}{5 / 36}=\frac{2}{5}$