Practice Questions
Concept Explanation
A standard deck has 52 cards: 4 suits (hearts, diamonds, clubs, spades) with 13 ranks each (Ace through King).
Key Counts
- Red cards = 26; Black cards = 26
- Face cards (J, Q, K) = 12; Aces = 4
- P(one card drawn) = favourable / 52
Example
P(king) = 4/52 = 1/13; P(heart) = 13/52 = 1/4.
Common Trap
Confirm whether the deck is standard 52 cards with no jokers unless stated.
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Q1 EasyOne card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a heart?ExplanationA standard deck has 52 cards and 13 hearts. Using P(E) = favourable / total, P(heart) = 13/52 = 1/4. Hence the answer is 1/4.
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Q2 EasyOne card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?ExplanationFace cards are Jack, Queen and King in each of 4 suits, so favourable = 3 × 4 = 12. P(face card) = 12/52 = 3/13. Hence the answer is 3/13.
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Q3 EasyOne card is drawn from a standard deck. What is P(king of hearts)?ExplanationThere is exactly one king of hearts in 52 cards. P = 1/52. Hence the answer is 1/52.
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Q4 EasyOne card is drawn from a pack of 52 cards. What is the probability that it is an ace?ExplanationThere are 4 aces in a deck of 52. P(ace) = 4/52 = 1/13. Hence the answer is 1/13.
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Q5 EasyOne card is drawn. What is the probability that it is a black card?ExplanationBlack cards = clubs + spades = 26. P(black) = 26/52 = 1/2. Hence the answer is 1/2.
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Q6 EasyA card is drawn from a pack of 52 cards. The probability of getting a red card is:ExplanationRed cards = hearts + diamonds = 26. P(red) = 26/52 = 1/2. Hence the answer is 1/2.
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Q7 EasyOne card is drawn at random from a pack of 52 cards. What is the probability that it is a spade?ExplanationThere are 13 spades. P(spade) = 13/52 = 1/4. Hence the answer is 1/4.
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Q8 MediumOne card is drawn. What is P(not a spade)?ExplanationNon-spades = 52 − 13 = 39. P(not spade) = 39/52 = 3/4. Hence the answer is 3/4.
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Q9 MediumA fresher paper asks: one card is drawn. What is P(red king)?ExplanationRed kings are king of hearts and king of diamonds (2 cards). P = 2/52 = 1/26. Hence the answer is 1/26.
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Q10 MediumOne card is drawn from a pack of 52 cards. What is the probability of getting the queen of clubs or the king of hearts?ExplanationThese are two specific distinct cards. Favourable = 2, total = 52. P = 2/52 = 1/26. Hence the answer is 1/26.
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Q11 MediumOne card is drawn. What is P(king or ace)?ExplanationKings and aces are disjoint: 4 + 4 = 8 favourable cards. P = 8/52 = 2/13. Hence the answer is 2/13.
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Q12 HardTwo cards are drawn at random from a pack of 52 cards without replacement. What is P(both are aces)?ExplanationWithout replacement: P = C(4,2) / C(52,2) = 6 / 1326 = 1/221. Sequentially: (4/52) × (3/51) = 12/2652 = 1/221. Hence the answer is 1/221.
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Q13 HardTwo cards are drawn without replacement from a pack of 52. What is P(one red and one black)?ExplanationCases: red then black, or black then red. P = 2 × (26/52) × (26/51) = 26/51. Equivalently C(26,1)×C(26,1)/C(52,2) = 676/1326 = 26/51. Hence the answer is 26/51.
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Q14 HardTwo cards are drawn at random from a pack of 52 cards. What is the probability that both the cards are kings?ExplanationThere are 4 kings. Without replacement, P(both kings) = C(4,2)/C(52,2) = 6/1326 = 1/221. Or (4/52)×(3/51) = 1/221. Hence the answer is 1/221.
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DS1 Easy
In a campus quiz, what is P(drawing a king from the deck)?
Statement IA standard 52-card deck is used and one card is drawn at random.
Statement IIThere are exactly 4 kings in the deck.
ExplanationStatement I alone (standard deck has 4 kings): P = 4/52 = 1/13. Statement II alone lacks the total number of cards. Answer: A. -
DS2 Easy
What is P(drawing a red card)?
Statement IHalf of the cards in the pack are red.
Statement IIThere are 26 red cards in a pack of 52.
ExplanationI: P(red) = 1/2. II: P(red) = 26/52 = 1/2. Either alone is sufficient. Answer: D.
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DS3 Medium
What is P(drawing a face card from a standard deck)?
Statement IFace cards are defined as Jack, Queen and King of each suit.
Statement IIOne card is drawn at random from 52 cards.
ExplanationI alone gives 12 face cards but needs total outcomes. II alone gives the sample space but not the face-card count. Together: P = 12/52 = 3/13. Answer: C. -
DS4 Hard
What is P(drawing both aces when two cards are drawn without replacement)?
Statement IA standard pack of 52 cards with 4 aces is used.
Statement IIThe draws are without replacement.
ExplanationI alone does not confirm with/without replacement. II alone lacks the deck composition. Together: P = (4/52)×(3/51) = 1/221. Answer: C.