From a pack of 52 playing cards Jacks, queens, kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is a black queen.

Given:

From a pack of 52 playing cards Jacks, queens, kings and aces of red colour are removed.

From the remaining, a card is drawn at random.

To do:

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

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 Jacks, queens, kings and aces of red colour 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 cards that are black queens 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 that the card drawn is a black queen $=\frac{2}{44}$

$=\frac{1}{22}$

The probability that the card drawn is a black queen is $\frac{1}{22}$.      

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Updated on: 10-Oct-2022

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