Question:
Out of 50 tickets numbered 00, 01, 02, …, 49, one ticket is drawn randomly. The probability that the ticket has the product of its digits 7, given that the sum of the digits is 8, is
Out of 50 tickets numbered 00, 01, 02, …, 49, one ticket is drawn randomly. The probability that the ticket has the product of its digits 7, given that the sum of the digits is 8, is
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List outcomes carefully when digits are involved.
Updated On: Apr 23, 2026
- $\frac{1}{14}$
- $\frac{3}{14}$
- $\frac{1}{5}$
- None of these
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The Correct Option is C
Solution and Explanation
Concept:
Conditional probability = Favorable Total (given condition)
Step 1: Condition: sum of digits = 8.
Possible pairs (tens, units): \[ (0,8),(1,7),(2,6),(3,5),(4,4) \]
Step 2: Total outcomes = 5.
Step 3: Product = 7 only for: \[ (1,7) \]
Step 4: Favorable outcomes = 1.
Step 5: Probability: \[ P = \frac{1}{5} \] Conclusion:
Answer = $\frac{1}{5}$
Step 1: Condition: sum of digits = 8.
Possible pairs (tens, units): \[ (0,8),(1,7),(2,6),(3,5),(4,4) \]
Step 2: Total outcomes = 5.
Step 3: Product = 7 only for: \[ (1,7) \]
Step 4: Favorable outcomes = 1.
Step 5: Probability: \[ P = \frac{1}{5} \] Conclusion:
Answer = $\frac{1}{5}$
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