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Question
All jacks, queens and kings 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 red card.
Solution
In a pack of 52 playing cards, there are 4 jack, 4 queen and 4 king cards.
All jack, queen and king cards are removed from the pack. Then,
Number of remaining cards = 52 − 12 = 40
∴ Total number of outcomes = 40
There are 2 red jacks, 2 red queens and 2 red kings among 4 jack, 4 queen and 4 king cards removed from the pack.
Number of red cards in the remaining pack of cards = 26 − (2 + 2 + 2) = 20
So, the favourable number of outcomes are 20.
∴ P(drawing a red card) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{20}{40} = \frac{1}{2}\]
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