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,…

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

Aicharya · 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}

Paragraph: Box $1$ contains three cards bearing numbers $1,2,3$; box $2$ contains five cards bearing numbers…

Solution