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Theoretical Probability

A card is dra...

Question

A card is drawn at random from a pack of 52 cards. Find the probaility 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

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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 = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence the probability of getting a black king is equal to 2/52=1/26

(ii) Total number of black cards is 26

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

Hence the total number of black card or king will be 26+2 = 28

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

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

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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

Total number of a jack, queen and king are 12

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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.

Total number of cards that are a heart and a kingie equal to 13 + 3 = 16

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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 spade cards.

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards that is spade or an ace = 16/52=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 4 + 4 = 8

Hence Total number of cards that are neither an ace nor a king is 52 – 8 = 44

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards neither an ace nor a king = 44/52=11/13

(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 26+2 = 28

Hence Total number of cards that are neither a red nor a queen= 52 -28 = 24

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting neither a red card nor a queen is equal to 24/52=6/13

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 = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a black king is equal to 2/52=1/26

(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 26+2 = 28

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a black cards or a king = 28/52=7/13

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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

Total number of a jack, queen and king are 12

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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.

Total number of cards that are a heart and a kingie equal to 13 + 3 = 16

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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 spade cards.

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards that is spade or an ace = 16/52=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 4 + 4 = 8

Hence Total number of cards that are neither an ace nor a king is 52 – 8 = 44

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards neither an ace nor a king = 44/52=11/13

(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 26+2 = 28

Hence Total number of cards that are neither a red nor a queen= 52 -28 = 24

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting neither a red card nor a queen is equal to 24/52=6/13

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 = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a black king is equal to 2/52=1/26

(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 26+2 = 28

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a black cards or a king = 28/52=7/13

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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

Total number of a jack, queen and king are 12

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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.

Total number of cards that are a heart and a kingie equal to 13 + 3 = 16

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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 spade cards.

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards that is spade or an ace = 16/52=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 4 + 4 = 8

Hence Total number of cards that are neither an ace nor a king is 52 – 8 = 44

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards neither an ace nor a king = 44/52=11/13

(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 26+2 = 28

Hence Total number of cards that are neither a red nor a queen= 52 -28 = 24

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting neither a red card nor a queen is equal to 24/52=6/13

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 = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a black king is equal to 2/52=1/26

(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 26+2 = 28

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a black cards or a king = 28/52=7/13

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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

Total number of a jack, queen and king are 12

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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.

Total number of cards that are a heart and a kingie equal to 13 + 3 = 16

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence 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 spade cards.

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards that is spade or an ace = 16/52=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 4 + 4 = 8

Hence Total number of cards that are neither an ace nor a king is 52 – 8 = 44

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting cards neither an ace nor a king = 44/52=11/13

(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 26+2 = 28

Hence Total number of cards that are neither a red nor a queen= 52 -28 = 24

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting neither a red card nor a queen is equal to 24/52=6/13

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

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting other than ace is 48/52=12/13

(x) Total number of ten is 4

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a ten is 4/52=1/13

(xi) Total number of spade is 13

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a spade = 13/52=1/4

(xii) Total number of black cards is 26

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting black cards is 26/52=1/2

(xiii) Total number of 7 of club is 1

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a 7 of club is equal to = 1/52

(xiv) Total number of jacks are 4

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting jack 4/52=1/13

(xv) Total number of ace of spade is 1

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a ace of spade = 1/52

(xvi) Total number of queen is 4

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a queen is 4/52=1/13

(xvii) Total number of heart cards is 13

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a heart cards = 13/52=1/4

(xviii) Total number of red cards is 26

We know that PROBABILITY = $= \frac{N u m b e r o f f a v o r a b l e e v e n t}{T o t a l n u m b e r o f e v e n t}$

Hence probability of getting a red cards = 26/52=1/2

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Similar questions

Q. A card is drawn at random from a pack of

52

cards. Find the probability that the card is drawn is
(i) a black king (ii) either a black card or a king (iii) a jack, queen or a king (iv) neither an ace nor a king (v) spade or an ace (vi) neither a red card nor a queen (vii) other than an ace (viii) a ten (ix) a spade (x) a black card (xi) the seven of clubs (xii) jack (xiii) the ace of spades (xiv) a queen (xv) a heart (xvi) a red card (xvii) neither a king nor a queen

Q. 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

Q. A card is drawn at random from a well-shuffled deck of

52

playing cards. Find the probability that the card drawn is (i) a card of spades or an ace, (ii) a black king, (iii) neither a jack nor a king, (iv) either a king or a queen.

Q. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(a) (i)

a king of red colour

(i i)

(i i i)

A red face card

(i v)

A jack of hearts

(b) (i)

(i i)

the queen of diamonds

(i i i)

Neither a red card nor a queen

(c) (i)

A non-face card

(i i)

a black king or a red queen

Q. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability that the card drawn is (a) a king or a jack (b) a red card (c) neither a king nor a queen.

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