# All the Black Face Cards Are Removed from a Pack of 52 Cards. the Remaining Cards Are Well Shuffled and Then a Card is Drawn at Random. Find the Probability of Getting Face Card - Mathematics

Sum

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting face card

#### Solution

In a pack of 52 playing cards, there are 2 black jacks, 2 black queens and 2 black kings.
All the black face cards are removed from the pack. Then,
Number of remaining cards = 52 − 6 = 46
∴ Total number of outcomes = 46

There are 6 face cards (2 red jacks, 2 red queens and 2 red kings) in the remaining pack of cards.
So, the favourable number of outcomes are 6.
∴ P(getting a face card) = $\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes } = \frac{6}{46} = \frac{3}{23}$

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 16 Probability
Exercise 16.1 | Q 65.1 | Page 26