Question

Q. 31. A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that
the drawn card is:
i. a card of spade ii. Either a king or a queen
Hii neither a jack nor a king​

Answer 1

Answer:

There are 52 cards in total.

Hence, total Outcomes =52

(i) Probability of the card drawn is a card of spade or an Ace:

Total cards of Spade =13

Total Aces =4

Number of Aces of Spade =1

Therefore,

Probability of the card drawn is a card of spade or an Ace:

52

13

+

52

4

−

52

1

=

52

16

=

13

4

(ii) Probability of the card drawn is a black king:

Total black kings: 2

Probability of the card drawn is a black king:

52

2

=

26

1

(iii) Probability of the card drawn is neither a jack nor a king

Total jacks =4

Total Kings =4

Probability of the card drawn is neither a jack nor a king:

1−

52

4+4

=

13

11

(iv) Probability of the card drawn is either a king or a queen:

Total Queens =4

Total Kings =4

Probability of the card drawn is either a king or a queen:

4+4

=

13

2

Answer 2

Answer:

(i). $\frac{1}{4}$ ; (ii). $\frac{2}{13}$ ; (iii). $\frac{11}{13}$

Step-by-step explanation:

(i). There are 13 cards of spade in a deck of 52 cards.

Total outcome is 52 and favorable outcome is 13 ⇒ The probability that the drawn card is a card of spade is

$\frac{13}{52}$ = $\frac{1}{4}$

(ii). There are 8 cards of a king and a queen in a deck of 52 cards.

Total outcome is 52 and favorable outcome is 8 ⇒ The probability that the drawn card is either a king or a queen is

$\frac{8}{52}$ = $\frac{2}{13}$

(iii). There are 8 cards of a jack and a king in a deck of 52 cards.

Total outcome is 52 and favorable outcome is (52 - 8) = 44 ⇒ The probability that the drawn card is neither a jack nor a king is

$\frac{44}{52}$ = $\frac{11}{13}$