Question:
In a class of 25 students with Roll Nos. 1 to 25, a student is picked up at random to answer a question. Find the probability that the roll number of the selected student is either a multiple of 5 or 7.
In a class of 25 students with Roll Nos. 1 to 25, a student is picked up at random to answer a question. Find the probability that the roll number of the selected student is either a multiple of 5 or 7.
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Use the principle of inclusion-exclusion to avoid double-counting when calculating probabilities of multiple conditions.
Updated On: Mar 7, 2025
- \( \frac{6}{25} \)
- \( \frac{4}{25} \)
- \( \frac{8}{25} \)
- \( \frac{7}{25} \)
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The Correct Option is C
Solution and Explanation
The total number of students is 25.
Multiples of 5 within this range: \[ 5, 10, 15, 20, 25 \quad \Rightarrow \quad 5 \text{ numbers} \] Multiples of 7 within this range: \[ 7, 14, 21 \quad \Rightarrow \quad 3 \text{ numbers} \] Common multiples of both 5 and 7 (LCM = 35) are not in the range.
Thus, the total favorable cases: \[ 5 + 3 = 8 \] Probability: \[ \frac{8}{25} \]
Multiples of 5 within this range: \[ 5, 10, 15, 20, 25 \quad \Rightarrow \quad 5 \text{ numbers} \] Multiples of 7 within this range: \[ 7, 14, 21 \quad \Rightarrow \quad 3 \text{ numbers} \] Common multiples of both 5 and 7 (LCM = 35) are not in the range.
Thus, the total favorable cases: \[ 5 + 3 = 8 \] Probability: \[ \frac{8}{25} \]
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