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17 Nov 2023, 02:30
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D
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Difficulty:
75%
(hard)
Question Stats:
65% (03:00) correct
35%
(02:52)
wrong
based on 146
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A bag has 24 cards labelled with numbers 1 to 24. All of the cards have different numbers on them. Maria draws 3 cards randomly. What is the probability that the numbers on the 3 cards are in arithmetic progression with the common difference 1 or 2?
(A) 5/506
(B) 3/253
(C) 4/223
(D) 21/1,012
(E) 29/1,012
(A) 5/506
(B) 3/253
(C) 4/223
(D) 21/1,012
(E) 29/1,012
19 Nov 2023, 16:09
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Case 1: 3 cards in arithmetic progression with the common difference 1: 22
1 2 3
2 3 4
...
22 23 24
Case 1: 3 cards in arithmetic progression with the common difference 2: 20
1 3 5
2 4 6
...
20 22 24
Ways to draw 3 cards from 24: 24C3 = 24*23*22/(3*2*1)= 4*23*22
The probability that the numbers on the 3 cards are in arithmetic progression with the common difference 1 or 2:
(22 + 20)/ 4*23*22 = 21/1012
Answer: D
1 2 3
2 3 4
...
22 23 24
Case 1: 3 cards in arithmetic progression with the common difference 2: 20
1 3 5
2 4 6
...
20 22 24
Ways to draw 3 cards from 24: 24C3 = 24*23*22/(3*2*1)= 4*23*22
The probability that the numbers on the 3 cards are in arithmetic progression with the common difference 1 or 2:
(22 + 20)/ 4*23*22 = 21/1012
Answer: D
General Discussion
20 Apr 2025, 06:41
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Why is this approach incorrect?
Choosing AP with difference 1 [x]: (22/24)*(1/23)*(1/22)
Choosing AP with difference 2 [y]: (20/24)*(1/23)*(1/22)
Final answer= x+y
Choosing AP with difference 1 [x]: (22/24)*(1/23)*(1/22)
Choosing AP with difference 2 [y]: (20/24)*(1/23)*(1/22)
Final answer= x+y
