 # All kings, queens and aces are removed from a pack of 52 cards.

Question:

All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is drawn from it. Find the probability that the drawn card is

(i) a black face card,
(ii) a red card.

Solution:

There are 4 kings, 4 queens and 4 aces. These are removed.

Thus, remaining number of cards = 52 − 4 − 4 − 4 = 40.

(i) Number of black face cards now = 2 (only black jacks).

$\therefore \mathrm{P}($ getting a black face card) $)=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$

$=\frac{2}{40}=\frac{1}{20}$

Thus, the probability that the drawn card is a black face card is $\frac{1}{20}$.

(ii) Number of red cards now = 26 − 6 = 20.

$\therefore \mathrm{P}($ getting a red card $)=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$

$=\frac{20}{40}=\frac{1}{2}$

Thus, the probability that the drawn card is a red card is $\frac{1}{2}$.