One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) a red face card
(iv) the jack of hearts
(v) a spade
(vi) the queen of diamonds

Given:

One card is drawn from a well shuffled deck of 52 cards.

To do:

We have to find the probability of getting 

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(v) a spade

(vi) the queen of diamonds

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.

This implies,

The total number of possible outcomes $n=52$.

(i) Number of cards that are king of red colour $=2$

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 king of red colour $=\frac{2}{52}$

$=\frac{1}{26}$

The probability of getting a king of red colour is $\frac{1}{26}$.  

(ii) Number of cards that are face cards(Kings, Queens, Jacks) $=3\times4=12$

Total number of favourable outcomes $=12$.

We know that,

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

Therefore,

Probability of getting a face card$=\frac{12}{52}$

$=\frac{3}{13}$

The probability of getting a face card is $\frac{3}{13}$.        

(iii) Number of cards that are face cards(Kings, Queens, Jacks) $=3\times2=6$

Total number of favourable outcomes $=6$.

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$=\frac{6}{52}$

$=\frac{3}{26}$

The probability of getting a red face card is $\frac{3}{26}$.         

(iv) Number of cards that are jack of hearts $=1$

Total number of favourable outcomes $=1$.

We know that,

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

Therefore,

Probability of getting a jack of hearts $=\frac{1}{52}$

The probability of getting a jack of hearts is $\frac{1}{52}$.    

(v) Number of cards that are spades $=13$

Total number of favourable outcomes $=13$.

We know that,

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

Therefore,

Probability of getting a spade $=\frac{13}{52}$

$=\frac{1}{4}$

The probability of getting a spade is $\frac{1}{4}$.     

(vi) Number of cards that are the queen of diamonds $=1$

Total number of favourable outcomes $=1$.

We know that,

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

Therefore,

Probability of getting the queen of diamonds $=\frac{1}{52}$

The probability of getting the queen of diamonds is $\frac{1}{52}$.