All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is a red card.

Given:

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them.

To do:

We have to find the probability that the drawn card is a red 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 the red face cards are removed.

This implies,

The total number of remaining cards $=52-3\times2=52-6=46$

The total number of possible outcomes $n=46$.

Number of red cards among the remaining cards $=26-6=20$

Total number of favourable outcomes $=26$.

We know that,

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

Therefore,

Probability of getting a red card $=\frac{20}{46}$

$=\frac{10}{23}$

The probability of getting a red card is $\frac{10}{23}$.       

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Updated on: 10-Oct-2022

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