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 red face card.

Given:

All kings and queens are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random.

To do:

We have to find the probability that this card is a red face card.

Solution:

A pack of cards contains 52 cards of four suits and two colours red and black.

Four suits are named as spades, hearts, diamonds, and clubs.

Each suit consists of one ace, one king, one queen, one jack and 9 other cards numbered from 2 to 10.

From a pack of 52 playing cards, all kings and queens are removed.

This implies,

The total number of remaining cards $=52-4\times2=52-8=44$

The total number of possible outcomes $n=44$.

Number of red face cards among the remaining cards $=2$

Total number of favourable outcomes $=2$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability of getting a red face card $=\frac{2}{44}$

$=\frac{1}{22}$

The probability of getting a red face card is $\frac{1}{22}$.       

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Updated on: 10-Oct-2022

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