A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled…
2011
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?
- A.
1/5
- B.
4/25
- C.
1/4
- D.
2/5
Attempted by 59 students.
Show answer & explanation
Correct answer: A
Key insight: order matters — the first card and the second card are distinguished.
Total ordered outcomes: 5 × 4 = 20 (choose the first card in 5 ways, then the second card in 4 remaining ways).
Favorable ordered outcomes: pairs where the first is exactly one greater than the second. These are (2,1), (3,2), (4,3), (5,4), which gives 4 outcomes.
Probability = favorable / total = 4/20 = 1/5.
Answer: 1/5