Box 1 contains three cards bearing numbers 1,2,3; box 2 contains five cards bearing numbers 1,2,3,4,5; and box 3 contains seven cards bearing numbers 1,2,3,4,5,6,7. A card is drawn from each of the boxes. Let be the number on the card drawn from the box, .
The probability that are in an arithmetic progression, is
The probability that are in an arithmetic progression, is
- (A)
- (B)
- (C)✓ Correct
- (D)
Answer: (C)
Solution
For to be in AP, we need .
Enumerating all favorable cases:
(1,1,1), (1,2,3), (1,3,5), (1,4,7), (2,2,2), (2,3,4), (2,4,6), (3,3,3), (3,4,5), (3,5,7), (3,2,1)
Total favorable cases = 11.
Total outcomes = .
Probability = .
Enumerating all favorable cases:
(1,1,1), (1,2,3), (1,3,5), (1,4,7), (2,2,2), (2,3,4), (2,4,6), (3,3,3), (3,4,5), (3,5,7), (3,2,1)
Total favorable cases = 11.
Total outcomes = .
Probability = .
JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option