UGC NET Questions (Paper – 1)

A fair coin has two equally likely outcomes: head (H) and tail (T). The sample space thus contains two outcomes, and only one of them is a head. Probability is calculated as favourable outcomes divided by total outcomes, so P(H) = 1/2. Therefore, the probability of getting a head in a single toss is 1/2.

Option A:
Option A is correct because it directly follows from the definition of probability for equally likely events. With two outcomes and one favourable event, the fraction must be 1/2. This is one of the most basic probabilities and forms the foundation for more complex problems involving coins and other experiments.

Option B:
A probability of 1/3 would imply that there are three equally likely outcomes, only one of which is a head. However, a standard coin has only two sides, so this interpretation is impossible in this context. Hence, 1/3 cannot be correct.

Option C:
A probability of 1/4 suggests four equally likely outcomes, which might occur in other experiments but not with a single coin toss. Since there are only two outcomes here, 1/4 misrepresents the situation. Therefore, it is not the correct answer.

Option D:
A probability of 2/3 would mean that heads are more likely than tails, which contradicts the assumption of a fair coin with equal chances. The probability must be symmetric between head and tail, making 2/3 an invalid option.