Exams › JEE Advanced › Maths
Three boxes contain cards with numbers: Box 1 has cards numbered 1, 2, 3; Box 2 has cards numbered 1, 2, 3, 4, 5; and Box 3 has cards numbered 1, 2, 3, 4, 5, 6, 7. A card is selected from each box. Let xᵢ represent the number on the card picked from the iᵗʰ box (i = 1, 2, 3). What is the probability that the numbers x₁, x₂, x₃ form an arithmetic sequence?
- 9/105
- 10/105
- 11/105
- 7/105
Correct answer: 11/105
Solution
For x₁, x₂, x₃ to form an arithmetic sequence, the condition 2x₂ = x₁ + x₃ must hold. By counting all possible combinations of cards from the three boxes and identifying those that satisfy this condition, the probability is calculated as 11 favorable outcomes out of 105 total outcomes, giving 11/105.
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