Discussion Forum

Box I contains three cards bearing numbers 1,2,3: box II  contains five cards bearing numbers 1,2,3,4,5  and box III  contained 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 numbers on the card drawn from i th box i=1,2,3.

The probability that x₁ +x₂+x₃  is odd is

Answer:

Explanation:

 Plan 

  Probability =  Number of favourable outcomes /  Number of total outcomes

  As   x₁ +x₂+x₃  is odd 

 So, all may be odd or one  of them is odd and other two are even

 $\therefore$ Required probability

$\frac{^{2}C_{1}\times^{3}C_{1}\times^{4}C_{1}+^{1}C_{1}\times^{2}C_{1}\times^{4}C_{1}+^{2}C_{1}\times^{2}C_{1}\times^{3}C_{1}+^{1}C_{1}\times^{3}C_{1}\times^{3}C_{1}}{^{3}C_{1}\times^{5}C_{1}\times^{7}C_{1}}$

        = $\frac{24+8+12+9}{105}=\frac{53}{105}$