A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{1}{8}$ ##
Let $E_1 = \text{Event for getting an even number on the die}$
and $E_2 = \text{Event that a spade card is selected}$
$∴P(E_1) = \frac{3}{6} = \frac{1}{2} \text{ and } P(E_2) = \frac{13}{52} = \frac{1}{4}$
Then, $P(E_1 \cap E_2) = P(E_1) \cdot P(E_2) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$