JEE Advanced2014MathematicsProbabilityActual
Paragraph: 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 x_ i be the number on the card drawn from the i^ t h box, i=1,2,3 . Question: The probability that x₁+x₂+x₃ is odd, is
Options
- A29 105
- B53 105
- C57 105
- D1 2
Correct answer
B. 53 105
Step-by-step solution
Case I: One odd, 2 even Total number of ways = 2 × 2 × 3 + 1 × 3 × 3 + 1 × 2 × 4 = 29 Case II: All 3 odd Number of ways = 2 × 3 × 4 = 24 Favourable ways = 53 Required probability = 53 3 × 5 × 7 = 53 105