Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is a king.

Given:

Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them.

To do:

We have to find the probability that the card drawn is a king.

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, red queens and black jacks are removed.

This implies,

The total number of remaining cards $=52-(2+2)=52-4=48$

The total number of possible outcomes $n=48$.

Number of kings among the remaining cards $=4$

Total number of favourable outcomes $=4$.

We know that,

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

Therefore,

Probability of getting a king $=\frac{4}{48}$

$=\frac{1}{12}$

The probability of getting a king is $\frac{1}{12}$.        

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Updated on: 10-Oct-2022

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