Given: A card is drawn at random from a pack of 52 cards

Required to Find: Probability of the following

Total number of cards in a pack = 52

(i) Number of cards which are black king = 2

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a black king = 2/52 = 1/26

(ii) Total number of black cards is (13 + 13) = 26

Total number of kings are 4 in which 2 black kings are also included.

So, the total number of black cards or king will be 26+2 = 28

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a black cards or a king = 28/52 = 7/13

(iii) Total number of cards which are black and a king cards is 2

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a black cards and a king is 2/52 = 1/26

(iv) A jack, queen or a king are 3 from each 4 suits.

So, the total number of a jack, queen and king are 12.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a jack, queen or a king is 12/52 = 3/13

(v) Total number of heart cards are 13 and king are 4 in which king of heart is also included.

So, the total number of cards that are a heart and a king = 13 + 3 = 16

Hence, the total number of cards that are neither a heart nor a king = 52 – 16 = 36

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting cards neither a heart nor a king = 36/52 = 9/13

(vi) Total number of spade cards is 13

Total number of aces are 4 in which ace of spade is included in the number of spade cards.

Hence, the total number of card which are spade or ace = 13 + 3 = 16

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting cards that is spade or an ace = 16/52 = 4/13

(vii) Total number of ace cards are 4 and king are 4

Total number of cards that are an ace or a king = 4 + 4 = 8

So, the total number of cards that are neither an ace nor a king is 52 – 8 = 44

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting cards which are neither an ace nor a king = 44/52 = 11/13

(viii) It’s know that the total number of red cards is 26.

Total number of queens are 4 in which 2 red queens are also included

Hence, total number of red cards or queen will be 26 + 2 = 28

So, the total number of cards that are neither a red nor a queen= 52 -28 = 24

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting neither a red card nor a queen = 24/52 = 6/13

(ix) Total number of card other than ace is 52 – 4 = 48

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting other than ace = 48/52 = 12/13

(x) Total number of tens in the pack of cards is 4.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a ten = 4/52 = 1/13

(xi) Total number of spade is 13

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a spade = 13/52 = 1/4

(xii) Total number of black cards in the pack is 26

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting black cards is 26/52 = 1/2

(xiii) Total number of 7 of club is 1 only.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a 7 of club = 1/52

(xiv) Total number of jacks are 4

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a jack = 4/52 = 1/13

(xv) Total number of ace of spade is 1

We know that Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting an ace of spade = 1/52

(xvi) Total number of queens is 4

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a queen = 4/52 = 1/13

(xvii) Total number of heart cards is 13

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a heart card = 13/52 = 1/4

(xviii) Total number of red cards is 26

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a red card = 26/52 = 1/2