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

Question

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 x 1 ​ + x 2 ​ + x 3 ​ is odd, is

TestHub · Accepted Answer

Case I: One odd, 2 even
Total number of ways $= 2 \times 2 \times 3 + 1 \times 3 \times 3 + 1 \times 2 \times 4 = 29$
Case II: All 3 odd
Number of ways $= 2 \times 3 \times 4 = 24$
Favourable ways = 53
Required probability $= \frac{53}{3 \times 5 \times 7} = \frac{53}{105}$

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