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Three boxes contain cards numbered as follows: the first box has cards numbered 1, 2, 3; the second box has cards numbered 1 through 5; and the third box has cards numbered 1 through 7. A single card is drawn from each box. Let xᵢ represent the number on the card picked from the iᵗʰ box, where i = 1, 2, 3. What is the probability that the sum x₁ + x₂ + x₃ is an odd number?
- 29/105
- 53/105
- 57/105
- 1/2
Correct answer: 53/105
Solution
The sum x₁ + x₂ + x₃ is odd if an odd number of the selected cards are odd. Calculating the probabilities for all valid cases gives a total probability of 53/105.
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