# 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 - Mathematics

Sum

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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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 16 Probability
Exercise 16.1 | Q 68.2 | Page 26