Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
Mohan, Lata and Sudha are taking the SAT exam. The probabilities that Mohan, Lata and Sudha will pass the exam are 1/3, 2/5 and 3/4, respectively. What is the probability that exactly one of them will pass the exam?
Last updated May 30, 2026
Correct Answer:
Option B —
5/12
To find the probability that exactly one of them passes, we need to calculate three separate possibilities:
Mohan passes, while Lata and Sudha fail.
Lata passes, while Mohan and Sudha fail.
Sudha passes, while Mohan and Lata fail.
First, let us find the probability of each person failing by subtracting their passing probability from 1:
Probability that Mohan fails: 2/3
Probability that Lata fails: 3/5
Probability that Sudha fails: 1/4
Now, we calculate the probability for each of the three scenarios:
Scenario 1: Only Mohan passes
Multiply Mohan passing (1/3) by Lata failing (3/5) by Sudha failing (1/4).
1/3 times 3/5 times 1/4 equals 3/60.
Scenario 2: Only Lata passes
Multiply Mohan failing (2/3) by Lata passing (2/5) by Sudha failing (1/4).
2/3 times 2/5 times 1/4 equals 4/60.
Scenario 3: Only Sudha passes
Multiply Mohan failing (2/3) by Lata failing (3/5) by Sudha passing (3/4).
2/3 times 3/5 times 3/4 equals 18/60.
Total Probability
Finally, add the probabilities of these three independent scenarios together:
3/60 plus 4/60 plus 18/60 equals 25/60.
When we reduce the fraction 25/60 by dividing the top and bottom by 5, we get 5/12.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
