A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting a red ace.
Total number of all possible outcomes= 52
Number of red aces = 2
∴ P( getting a red ace) =`2/52 = 1/26`
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 king of red suit.
Total number of outcomes = 52
Let E1 be the event of getting a king of red suit.
Number of favourable outcomes = 2
∴ P(getting a king of red suit) = P(E1) = `("Number of outcomes favourable to" E_1)/ "Number of all possible outcomes"`
`= 2/52 = 1/26`
Thus, the probability of getting a king of red suit is `1/26`.
Concept: Probability - A Theoretical Approach
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Page 3
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 4
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 5
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 6
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 7
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 8
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 9
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 10
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 11
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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