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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) other than an ace

(x) a ten

(xi) a spade

(xii) a black card

(xiii) the seven of clubs

(xiv) jack

(xv) the ace of spades

(xvi) a queen

(xvii) a heart

(xviii) a red card

(xix) neither a king nor a queen

(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) other than an ace

(x) a ten

(xi) a spade

(xii) a black card

(xiii) the seven of clubs

(xiv) jack

(xv) the ace of spades

(xvi) a queen

(xvii) a heart

(xviii) a red card

(xix) neither a king nor a queen

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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 = $\frac{16}{52}=\overline{)\frac{4}{13}}$

(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 =

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