Question

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is: (i) a black king (ii) either a black card or a king (iii) black and a king (iv) a jack, queen or a king (v) neither a heart nor a king (vi) spade or an ace (vii) neither an ace nor a king (viii) neither a red card nor a queen (ix) the seven of clubs (x) a ten (xi) a spade (xii) a black card (xiii) a seven of clubs (xiv) jack (xv) the ace of spades (xvi) a queen (xvii) a heart (xviii) a red card Select the correct answer from above options

Answer 1

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