If a die is thrown and a card is selected at random from a deck of 52 playing cards, then the probability of getting an even number on the die and a spade card is

Let ${E_1} =$ Event for getting an even number on the die

and ${E_2} =$ Event that a spade card is selected
$\therefore$ $P\left( {{E_1}} \right) = \frac{3}{6} = \frac{1}{2}$ and $P\left( {{E_2}} \right) = \frac{{13}}{{52}} = \frac{1}{4}$

Then, $P\left( {{E_1} \cap {E_2}} \right) = P\left( {{E_1}} \right) \cdot P\left( {{E_2}} \right) = \frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8}$