Question

The king, the jack and the 10 spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling. Find the probability of getting a (1) red card (2) black jack (3) red king (4) 10 of hearts

Answer 1

Answer:

Given : The king, the jack and the 10 spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling.

To find : The probability of getting

(1) red card

(2) black jack

(3) red king

(4) 10 of hearts

Solution :

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}$

In a standard deck of 52 cards,

13 diamonds , 13 club , 13 hearts , 13 spade  in which 12 face cards

The king, the jack and the 10 spades are lost from a pack of 52 cards

Cards remaining are 52-1-1-10=40

(1) red card

→ If the king and jack is from red card then number of red cards = 24

Favorable outcome = 24

Total number of outcome = 40

Probability of a red card drawn is  

$\text{Probability}=\frac{24}{40}=\frac{3}{5}$

→ If the king and jack is not from red card then number of red cards = 26

Favorable outcome = 26

Total number of outcome = 40

Probability of a red card drawn is  

$\text{Probability}=\frac{26}{40}=\frac{13}{20}$

(2) black jack

→ If the jack is from black card then number of black cards = 25

Favorable outcome = 25

Total number of outcome = 40

Probability of black jack drawn is  

$\text{Probability}=\frac{25}{40}=\frac{5}{8}$

→ If the jack is not from black card then number of black cards = 26

Favorable outcome = 26

Total number of outcome = 40

Probability of black jack drawn is  

$\text{Probability}=\frac{26}{40}=\frac{13}{20}$

(3) red king

→ If the king is from red card then number of red cards = 25

Favorable outcome = 25

Total number of outcome = 40

Probability of red king drawn is  

$\text{Probability}=\frac{25}{40}=\frac{5}{8}$

→ If the king is not from red card then number of red cards = 26

Favorable outcome = 26

Total number of outcome = 40

Probability of red king drawn is  

$\text{Probability}=\frac{26}{40}=\frac{13}{20}$

(4) 10 of hearts

→ If the king and jack is from hearts then number of hearts cards = 8

Favorable outcome = 8

Total number of outcome = 40

Probability of 10 of hearts drawn is  

$\text{Probability}=\frac{8}{40}=\frac{1}{5}$

→ If the king and jack is from hearts then number of hearts cards = 10

Favorable outcome = 10

Total number of outcome = 40

Probability of 10 of hearts drawn is  

$\text{Probability}=\frac{10}{40}=\frac{1}{4}$

Answer 2

Step-by-step explanation:

Given : The king, the jack and the 10 spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling.

To find : The probability of getting

(1) red card

(2) black jack

(3) red king

(4) 10 of hearts

Solution :

\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}Probability=

Total number of outcome

Favorable outcome

In a standard deck of 52 cards,

13 diamonds , 13 club , 13 hearts , 13 spade in which 12 face cards

The king, the jack and the 10 spades are lost from a pack of 52 cards

Cards remaining are 52-1-1-10=40

(1) red card

→ If the king and jack is from red card then number of red cards = 24

Favorable outcome = 24

Total number of outcome = 40

Probability of a red card drawn is

\text{Probability}=\frac{24}{40}=\frac{3}{5}Probability=

40

24

=

5

3

→ If the king and jack is not from red card then number of red cards = 26

Favorable outcome = 26

Total number of outcome = 40

Probability of a red card drawn is

\text{Probability}=\frac{26}{40}=\frac{13}{20}Probability=

40

26

=

20

13

(2) black jack

→ If the jack is from black card then number of black cards = 25

Favorable outcome = 25

Total number of outcome = 40

Probability of black jack drawn is

\text{Probability}=\frac{25}{40}=\frac{5}{8}Probability=

40

25

=

8

5

→ If the jack is not from black card then number of black cards = 26

Favorable outcome = 26

Total number of outcome = 40

Probability of black jack drawn is

\text{Probability}=\frac{26}{40}=\frac{13}{20}Probability=

40

26

=

20

13

(3) red king

→ If the king is from red card then number of red cards = 25

Favorable outcome = 25

Total number of outcome = 40

Probability of red king drawn is

\text{Probability}=\frac{25}{40}=\frac{5}{8}Probability=

40

25

=

8

5

→ If the king is not from red card then number of red cards = 26

Favorable outcome = 26

Total number of outcome = 40

Probability of red king drawn is

\text{Probability}=\frac{26}{40}=\frac{13}{20}Probability=

40

26

=

20

13

(4) 10 of hearts

→ If the king and jack is from hearts then number of hearts cards = 8

Favorable outcome = 8

Total number of outcome = 40

Probability of 10 of hearts drawn is

\text{Probability}=\frac{8}{40}=\frac{1}{5}Probability=

40

8

=

5

1

→ If the king and jack is from hearts then number of hearts cards = 10

Favorable outcome = 10

Total number of outcome = 40

Probability of 10 of hearts drawn is

\text{Probability}=\frac{10}{40}=\frac{1}{4}Probability=

40

10

=

4

1