What is drawn from a well shuffled deck of 52 cards find the probability of getting a face card?

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

Total number of outcomes = 52

Let E2 be the event of getting a face card.

Number of favourable outcomes = 12

∴ P(getting a face card) = P(E2) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`

`= 12/52 = 3/13`

Thus, the probability of getting a face card is `3/13`.

Concept: Concept Or Properties of Probability

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Page 2

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

Total number of outcomes = 52

Let E3 be the event of getting a red face card.

Number of favourable outcomes = 6

∴ P(getting a red face card) = P(E3) = `("Number of outcomes favourable to" E_3)/"Number of all possible outcomes"`

`6/52 = 3/26`

Thus, the probability of getting a red face card is `3/26`.

Concept: Concept Or Properties of Probability

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Page 3

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

Total number of outcomes = 52

Let E4 be the event of getting a queen of black suit.Number of favourable outcomes = 2

∴ P(getting a queen of black suit) = P(E4) = `("Number of outcomes favourable to" E_4)/"Number of all possible outcomes"`

`=2/52 = 1/26`

Thus, the probability of getting a queen of black suit is `1/26`.

Concept: Concept Or Properties of Probability

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Page 4

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

Let E5 be the event of getting a jack of hearts.Number of favourable outcomes = 1

∴ P(getting a jack of hearts) = P(E5) = `("Number of outcomes favourable to" E_5)/"Number of all possible outcomes"`

`= 1/52`

Thus, the probability of getting a jack of hearts is `1/52`.

Concept: Concept Or Properties of Probability

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Page 5

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

Total number of outcomes = 52

Let E6 be the event of getting a spade.

Number of favourable outcomes = 13

∴ P(getting a spade) = P(E6) = `("Number of outcomes favourable to" E_6)/"Number of all possible outcomes"`

`=13/52 = 1/4`

Thus, the probability of getting a spade is `1/4`.

Concept: Concept Or Properties of Probability

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Page 6

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is a card of spades of an ace.

Total number of all possible outcomes= 52

Number of spade cards = 13

Number of aces = 4 (including 1 of spade)

Therefore, number of spade cards and aces = (13 + 4 − 1) = 16

 ∴ P( getting a spade or an ace card) = `16/52 = 4/13` 

Concept: Concept Or Properties of Probability

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Page 7

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is a red king.

Total number of all possible outcomes= 52

Number of  red kings = 2

∴ P( getting a red king) =`2/52 = 1/26`

Concept: Concept Or Properties of Probability

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Page 8

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is either a king or a queen.

Total number of all possible outcomes= 52

Total number of kings = 4

Total number of queens = 4

Let E be the event of getting either a king or a queen.

Then, the favourable outcomes =  4 + 4 = 8

∴ P( getting a king or a queen) = P (E) = `8/52 = 2/13`

Concept: Concept Or Properties of Probability

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Page 9

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is neither a king nor a queen.

Let E be the event of getting either a king or a queen. Then, (not E) is the event that drawn card is neither a king nor a queen.     

Then, P(getting a king or a queen ) = `2/13`

Now, ​P (E) + ​P (not E) = 1

∴ ​P(getting neither a king nor a queen ) = `1 - (2/13) = 11/13` 

Concept: Concept Or Properties of Probability

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