Question

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. The probability that x1+x2+x3 is odd is The probability that x1,x2,x3 are in an aritmetic progression is A. 29 105 B. 53 105 C. 57 105 D. 1 2 Select the correct answer from above options

Answer 1

Correct Answer - B Plan Probability = Number of favourable outcomes Number of total outcomes As x1+x2+x+3 is odd. So, all may be odd or one of them is odd and other two are even. ∴ Required probability (""^(2)C_1xx""^(3)C_1xx""^(4)C_1+""^(1)C_1xx""^(2)C_1xx""^(4)C_1+""^(2)C_1xx""^(2)C_1xx""^(3)C_1+""^(1)C_1xx""^(3)C_1xx""^(7)C_1)/(""^3C_1xx""^(5)C_1xx""^(7)C_1) (24+8+12+9)/(105) (53)/(105)