Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A biased dice has numbers from 1 to 6 written on its faces. The probability of occurrence of 1 when this dice is thrown is a non-positive number. The probability of occurrence of numbers from 2 to 6 is same for these 5 numbers. This dice is thrown once. What is the probability that an odd number appears on the dice?
Last updated May 30, 2026
Correct Answer:
Option B —
2/5
To find the probability of rolling an odd number, we can break the problem down logically based on the rules of probability.
Step 1: Determine the probability of rolling a 1
The problem states that the probability of rolling a 1 is a non-positive number. By definition, a probability can never be negative; the lowest possible probability is zero, which means an event is impossible. Therefore, the probability of rolling a 1 must be exactly zero.
Step 2: Find the probability for the remaining numbers
Since the total probability of all possible outcomes when rolling a dice must always equal 1, and the probability of rolling a 1 is zero, the remaining numbers from 2 to 6 must share the entire probability of 1.
We are told that the numbers 2, 3, 4, 5, and 6 all have the exact same chance of appearing. Since there are 5 of these numbers sharing a total probability of 1 equally, the probability of rolling any single one of them is 1 divided by 5, or 1/5.
Step 3: Calculate the probability of getting an odd number
The odd numbers on a standard dice are 1, 3, and 5. Let's look at their individual probabilities:
The probability of rolling a 1 is zero.
The probability of rolling a 3 is 1/5.
The probability of rolling a 5 is 1/5.
To find the total probability of getting any odd number, we add these probabilities together. Zero plus 1/5 plus 1/5 equals 2/5.
Therefore, the probability that an odd number appears on the dice is 2/5.
Correct Answer: (B) 2/5
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
