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 th box, i = 1, 2, 3.
(i) The probability that x 1 + x 2 + x 3 is odd, is
Text Solution
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(i)
Sol. x 1 + x 2 + x 3 is odd if all three are odd or 2 are even & one is odd
(OOO) or (OEE) or (EOE) or (EEO)
= 
(ii)
Sol. 2x 2 = x 1 + x 3 .
If x 1 & x 3 both are odd 2 × 4 = 8 ways
x 1 & x 3 both are even 1 × 3 = 3 ways
Total = 11 ways
Total (x 1 x 2 x 3 ) triplets are 3 × 5 × 7 ⇒ P = 
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