Question:
Cards marked with numbers 2 to 105 are placed in a box and mixed. One card is chosen at random. The probability that the number on the card is less than 15 is
Cards marked with numbers 2 to 105 are placed in a box and mixed. One card is chosen at random. The probability that the number on the card is less than 15 is
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Always use: count = last - first + 1 for inclusive sequences.
Updated On: Apr 30, 2026
- $\frac{1}{8}$
- $\frac{1}{9}$
- $\frac{7}{8}$
- $\frac{8}{9}$
- $\frac{2}{7}$
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The Correct Option is B
Solution and Explanation
Step 1: Total number of cards
Cards are numbered from 2 to 105: \[ \text{Total} = 105 - 2 + 1 = 104 \]
Step 2: Favorable outcomes
Numbers less than 15 are: \[ 2,3,4,\ldots,14 \] \[ \text{Count} = 14 - 2 + 1 = 13 \]
Step 3: Probability
\[ P = \frac{13}{104} \]
Step 4: Simplify
\[ \frac{13}{104} = \frac{1}{8} \] \[ \boxed{\frac{1}{8}} \]
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