# A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is

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

(vii) neither an ace nor a king

(viii) neither a red card nor a queen.

(ix) other than an ace

(x) a ten

(xii) a black card

(xiii) the seven of clubs

(xiv) jack

(xvi) a queen

(xvii) a heart

(xviii) a red card

(xix) neither a king nor a queen

Solution:

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

TO FIND: Probability of the following

Total number of cards = 52

(i) Cards which are black king is 2

We know that PROBABILITY = Hence probability of getting a black king is equal to (ii) Total number of black cards is 26

Total numbers of kings are 4 in which 2 black kings are also included

Hence total number of black card or king will be We know that PROBABILITY = Hence probability of getting a black cards or a king = (iii) Total number of black and a king cards is 2

We know that PROBABILITY = Hence probability of getting a black cards and a king is (iv) A jack, queen or a king are 3 from each 4 suits

Total number of a jack, queen and king are 12

We know that PROBABILITY = Hence probability of getting a jack, queen or a king is = (v) Total number of heart cards are 13 and king are 4 in which king of heart is also included.

Total number of cards that are a heart and a kingie equal to Hence Total number of cards that are neither a heart nor a king= We know that PROBABILITY = Hence probability of getting cards neither a heart nor a king = (vi) Total number of spade cards is 13

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

Hence total number of card which are spade or ace = We know that PROBABILITY = Hence probability of getting cards that is spade or an ace = 1652=413">1652=4131652=413

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

Total number of cards that are a ace and a king is equal to Hence Total number of cards that are neither an ace nor a kin is We know that PROBABILITY = Hence probability of getting cards neither an ace nor a king = (viii) Total number of red cards is 26

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

Hence total number of red card or queen will be Hence Total number of cards that are neither a red nor a queen= We know that PROBABILITY = Hence probability of getting neither a red card nor a queen is equal to (ix) Total number of card other than ace is We know that PROBABILITY = Hence probability of getting other than ace is (x) Total number of ten is 4

We know that PROBABILITY = Hence probability of getting a ten is (xi) Total number of spade is 13

We know that PROBABILITY = Hence probability of getting a spade = (xii) Total number of black cards is 26

We know that PROBABILITY = Hence probability of getting black cards is (xiii) Total number of 7 of club is 1

We know that PROBABILITY = Hence probability of getting a 7 of club is equal to (xiv) Total number of jack are 4

We know that PROBABILITY = Hence probability of getting jack (xv) Total number of ace of spade is 1

We know that PROBABILITY = Hence probability of getting a ace of spade (xvi) Total number of queen is 4

We know that PROBABILITY = Hence probability of getting a queen (xvii) Total number of heart cards is 13

We know that PROBABILITY = Hence probability of getting a heart cards = (xviii) Total number of red cards is 26

We know that PROBABILITY = Hence probability of getting a red cards = 