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Question
All kings and queens are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is randomly drawn from it. Find the probability that this card is a black card.
Solution
In a pack of 52 playing cards, there are 4 queen and 4 king cards.
All the king and queen cards are removed from the pack. Then,
Number of remaining cards = 52 − (4 + 4) = 44
∴ Total number of outcomes = 44
There are 2 black kings and 2 black queens among the 4 queen and 4 king cards removed from the pack of cards.
Number of black cards in the remaining pack of cards = 26 − 4 = 22
So, the favourable number of outcomes are 22.
∴ P(getting a black card) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{22}{44} = \frac{1}{2}\]
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