A card is drawn at random from a deck of 52 cards What is the probability of getting a black

(i) A black king

Total number of cards are 52 Number of black king cards = 2

Probability of getting black king cards is = Total number of black king cards/Total number of cards

= 2/52

= 1/26

∴ Probability of getting black king cards is 1/26

(ii) Either a black card or a king Total number of cards are 52

Number of either a black card or a king = 28

Probability of getting either a black card or a king is = Total number of either black or king card/Total number of cards

= 28/52

= 7/13

∴ Probability of getting either a black card or a king is 7/13

(iii) Black and a king

Total number of cards are 52 Number of black and a king = 2

Probability of getting black and a king is = Total number of black and king card/Total number of cards

= 2/52

= 1/26

∴ Probability of getting black and a king is 1/26

(iv) a jack, queen or a king Total number of cards are 52

Number of a jack, queen or a king = 12

Probability of getting a jack, queen or a king is = Total number of jack, queen or king card/Total number of cards

= 12/52

= 3/13

∴ Probability of getting a jack, queen or a king is 3/13

(v) Neither a heart nor a king Total numbers of cards are 52 Total number of heart cards = 13

Probability of getting a heart is = Total number of hearts/Total number of cards

= 13/52

= 1/4

Total number of king cards = 4

Probability of getting a king is = Total number of king card/Total number of cards

= 4/52

= 1/13

Total probability of getting a heart and a king = 13/52 + 4/52 – 1/52

= (13+4-1)/52

= 16/52

= 4/13

∴ Probability of getting neither a heart nor a king = 1 – 4/13 = (13-4)/13 = 9/13

(vi) Spade or an ace

Total numbers of cards are 52 Number of spade cards = 13

Probability of getting spade cards is = Total number of spade card/Total number of cards

= 13/52

Number of ace cards = 4

Probability of getting ace cards is = Total number of ace card/Total number of cards

= 4/52

= 1/13

Probability of getting ace and spade cards is = Total number of ace and spade card/Total number of cards

= 1/52

Probability of getting an ace or spade cards is = 13/52 + 4/52 – 1/52

= (13+4-1)/52

= 16/52

= 4/13

∴ Probability of getting an ace or spade cards is = 4/13

(vii) Neither an ace nor a king Total numbers of cards are 52 Number of king cards = 4

Number of ace cards = 4

Total number of cards = 4 + 4 = 8

Total number of neither an ace nor a king are = 52 – 8 = 44

Probability of getting neither an ace nor a king is = Total number of neither ace nor king card/Total number of cards

= 44/52

= 11/13

∴ Probability of getting neither an ace nor a king is 11/13

(viii) Neither a red card nor a queen Total numbers of cards are 52

Red cards include hearts and diamonds Number of hearts in a deck of 52 cards = 13 Number of diamonds in a deck of 52 cards = 13 Number of queen in a deck of 52 cards = 4

Total number of red card and queen = 13 + 13 + 2 = 28 [since queen of heart and queen of diamond are removed]

Number of card which is neither a red card nor a queen = 52 - 28 = 24

Probability of getting neither a king nor a queen is = Total number of neither red nor queen card/Total number of cards

= 24/52

= 6/13

∴ Probability of getting neither a king nor a queen is 6/13

(ix) Other than an ace

Total numbers of cards are 52 Total number of ace cards = 4

Total number of non-ace cards = 52-4 = 48

Probability of getting non-ace is = Total number of non-ace cards/Total number of cards

= 48/52

= 12/13

∴ Probability of getting non-ace card is 12/13

(x) A ten

Total numbers of cards are 52 Total number of ten cards = 4

Probability of getting ten cards is = Total number of ten cards/Total number of cards

= 4/52

= 1/13

∴ Probability of getting ten card is 1/13

(xi) A spade

Total numbers of cards are 52 Total number of spade cards = 13

Probability of getting spade is = Total number of spade cards/Total number of cards

= 13/52

= 1/4

∴ Probability of getting a spade is 1/4

(xii) A black card

Total numbers of cards are 52

Cards of spades and clubs are black cards. Number of spades = 13

Number of clubs = 13

Total number of black card out of 52 cards = 13 + 13 = 26

Probability of getting black cards is = Total number of black cards/Total number of cards

= 26/52

= 1/2

∴ Probability of getting a black card is 1/2

(xiii) The seven of clubs Total numbers of cards are 52

Total number of the seven of clubs cards = 1

Probability of getting the seven of clubs cards is = Total number of the seven of club cards/ Total numbers of cards

= 1/52

∴ Probability of the seven of club card is 1/52

(xiv) Jack

Total numbers of cards are 52 Total number of jack cards = 4

Probability of getting jack cards is = Total number of jack cards/ Total numbers of cards

= 4/52

= 1/13

∴ Probability of the jack card is 1/13

(xv) The ace of spades

Total numbers of cards are 52

Total number of the ace of spades cards = 1

Probability of getting ace of spade cards is = Total number of ace of spade cards/ Total numbers of cards

= 1/52

∴ Probability of the ace of spade card is 1/52

(xvi) A queen

Total numbers of cards are 52 Total number of queen cards = 4

Probability of getting queen cards is = Total number of queen cards/Total numbers of cards

= 4/52

= 1/13

∴ Probability of a queen card is 1/13

(xvii) A heart

Total numbers of cards are 52 Total number of heart cards = 13

Probability of getting queen cards is = Total number of heart cards/Total numbers of cards

= 13/52

= 1/4

∴ Probability of a heart card is 1/4

(xviii) A red card

Total numbers of cards are 52

Total number of red cards = 13+13 = 26

Probability of getting queen cards is = Total number of red cards/Total numbers of cards

= 26/52

= 1/2 ∴ Probability of a red card is 1/2

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a card is randomly selected from a deck of card. Find the probability that it is a black card or a face card

6 years ago

There are 52 cards in a deck in total. Of those 52 cards, there are four different suits (diamonds, hearts, clubs, spades). There are 13 cards in each of the different suits. Also, there are 3 face cards in each of the different suits (therefore, there are 12 face cards in total). Diamonds and Hearts are red cards (there are 26 total red cards) and Clubs and Spades are black cards (there are 26 total black cards).

There are 26 black cards and 12 face cards in total. However, of those 26 black cards, there are 6 face cards. That means there are 26+12-6 = 32 cards in total that are either a black card or a face card, but not both. That means the answer to the question is 32/52 = 8/13.

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6 years ago

A = number of black cards B = number of picture cards (or face cards) C = number of black picture cards

There are 26 black cards (spades and clubs), so A = 26.

There are 3 picture cards (Jack, Queen, King) in each suit. There are 4 suits (clubs, hearts, spades, diamonds). So there are 3*4 = 12 picture cards. This means B = 12

There are 2 suits which are black (spades and clubs) with 3 face cards per suit, so 2*3 = 6 cards which are both black cards and face cards. So C = 6

The number of cards that are either black cards or a face card, or both, is...

D = A+B-C D = 26+12-6

D = 32

So there are 32 cards that are either black cards or a face card, or both

This is out of 52 cards total, so

probability of selecting a black card or a picture card = D/52

probability of selecting a black card or a picture card = 32/52

probability of selecting a black card or a picture card = 8/13

The final answer, as a fraction, is 8/13

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