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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 xi be the number on the card drawn from the ith box, i = 1, 2, 3.
Q.
The probability that x1 , x2 , x3 are in an arithmetic progression, is
  • a)
    9/105
  • b)
    10/105
  • c)
    11/105
  • d)
    7/105
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Box 1 contains three cards bearing numbers 1, 2, 3 ; box 2 contains fi...
Here 2x2 = x1 + x3
x1 + x3 = even
Hence number of favourable ways = 
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Most Upvoted Answer
Box 1 contains three cards bearing numbers 1, 2, 3 ; box 2 contains fi...
Probability of x1, x2, x3 being in an arithmetic progression

Calculating the total number of outcomes:
- Total number of ways to draw a card from each box = 3 * 5 * 7 = 105

Calculating the number of favorable outcomes:
- For x1, x2, x3 to be in an arithmetic progression, there are 3 cases: (1, 2, 3), (2, 3, 4), (3, 4, 5)
- For each case, the probability of drawing the cards in the correct order from the boxes is 1/3 * 1/5 * 1/7 = 1/105
- Since there are 3 such cases, the total probability of x1, x2, x3 being in an arithmetic progression is 3 * 1/105 = 3/105 = 1/35
Therefore, the probability that x1, x2, x3 are in an arithmetic progression is 1/35, which is equivalent to 11/105. Hence, the correct answer is option 'C' (11/105).
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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 xi be the number on the card drawn from the ith box, i = 1, 2, 3.Q.The probability that x1 , x2 , x3 are in an arithmetic progression, isa)9/105b)10/105c)11/105d)7/105Correct answer is option 'C'. Can you explain this answer?
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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 xi be the number on the card drawn from the ith box, i = 1, 2, 3.Q.The probability that x1 , x2 , x3 are in an arithmetic progression, isa)9/105b)10/105c)11/105d)7/105Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 xi be the number on the card drawn from the ith box, i = 1, 2, 3.Q.The probability that x1 , x2 , x3 are in an arithmetic progression, isa)9/105b)10/105c)11/105d)7/105Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 xi be the number on the card drawn from the ith box, i = 1, 2, 3.Q.The probability that x1 , x2 , x3 are in an arithmetic progression, isa)9/105b)10/105c)11/105d)7/105Correct answer is option 'C'. Can you explain this answer?.
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