Deck of Cards Probability

Deck of Cards Probability:

It is a pack of 52 playing cards. It has four suits and 13 cards in each suit. The four suits represent the four seasons, while the 52 cards represent the 52 weeks in a year. The 13 cards per suit represent the thirteen lunar cycles. The four suits in playing cards are clubs, diamonds, hearts, and spades. Out of these four suits the clubs and spades are black in colour and diamond and hearts are red in colour. Therefore, there are 26 red and 26 black cards

The thirteen cards of each suit comprise of an Ace, 2, 3, 4, 5, 6, 7, 8, 9,10, J (Jack), Q (Queen) and K (King). The J, Q, K are Face Cards have a face is drawn in each card. Thus, there are 12 face cards 3 in each suit. They are also called Court Cards because they represent Kings, Queens and Jacks the members of the court in olden times.

An Ace cannot be considered a “face card,” for the simple reason that it has no face on it.

The numbered cards 2, 3, 4, 5, 6, 7, 8, 9, 10 i.e. 9 in each suit hence 36 cards in a pack.

So, in a deck of cards we have 4 Ace cards, 2 black and 2 red. 36 numbered cards, 18 red and 18 black. 12 Face cards 6 red and 6 black.

Illustration: A card is drawn from a well-shuffled deck of 52 playing cards. Find the probability of getting an ace

Solution: As there are four aces in the deck, So the number of favorable cases =4

Total Outcomes: 52

$P(Ace)=frac{No.;of ;favourable; outcomes}{Total ;outcomes}=frac{4}{52}=frac{1}{13}$

Illustration: A card is drawn from a well-shuffled deck of 52 playing cards. Find the probability of getting 2 of spades

Solution: As there is only one 2 of spades in the deck, So the number of favorable cases =1

Total Outcomes: 52

$P(2;of;Spade)=frac{No.;of ;favourable; outcomes}{Total ;outcomes}=frac{1}{52}$

Illustration: A card is drawn from a well-shuffled deck of 52 playing cards. Find the probability of getting a red queen

Solution: As there are two red queens one each of Hearts and Diamonds in the deck, So the number of favorable cases =2

Total Outcomes: 52

$P(Red;queen)=frac{No.;of ;favourable; outcomes}{Total ;outcomes}=frac{2}{52}=frac{1}{26}$

Illustration: A card is drawn from a well-shuffled deck of 52 playing cards. Find the probability of getting a face card

Solution: As there are 3 face cards in each suit and there are 4 suits (diamond, club, spade, heart) therefore there are 12 face cards in the deck, So the number of favorable cases =12

Total Outcomes: 52

$P(A;face;card)=frac{No.;of ;favourable; outcomes}{Total ;outcomes}=frac{12}{52}=frac{3}{13}$

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Sample Questions

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Question : 1

A card is drawn from a well shuffled pack of 52 cards. Find the probability of: a non - face card
A. $large dpi{120} fn_jvn large frac{12}{52}$	B. $large frac{2}{52}$	C. $large frac{40}{52}$	D. $large frac{12}{52}$
Right Option : C
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Question : 2

A card is drawn from a well shuffled pack of 52 cards. Find the probability of: a black face card:
A. $large frac{4}{52}$	B. $large dpi{120} fn_jvn large frac{8}{52}$	C. $large frac{1}{52}$	D. $large frac{6}{52}$
Right Option : D
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Question : 3

A card is drawn from a well shuffled pack of 52 cards. Find the probability of: a king of red colour
A. $large frac{4}{52}$	B. $large frac{2}{52}$	C. $large frac{1}{52}$	D. $large frac{10}{52}$
Right Option : B
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