UGC NET Questions (Paper – 1)

When a fair coin is tossed twice, the sample space has four equally likely outcomes: HH, HT, TH and TT. Exactly one head occurs in the outcomes HT and TH. There are therefore two favorable cases out of four possible outcomes. The required probability is the ratio of favorable outcomes to total outcomes, which is 2/4 = 1/2.

Option A:
Option A, 1/4, would represent the probability of a single specific outcome like HH or TT, not the event of exactly one head. It counts only one case instead of both HT and TH.

Option B:
Option B correctly identifies two favorable outcomes and divides by the four equally likely possibilities. This simplifies to 1/2, representing a fifty percent chance of getting exactly one head in two tosses.

Option C:
Option C, 3/4, would mean that three of the four outcomes give exactly one head, but HH and TT clearly do not fit that description. It overestimates the probability.

Option D:
Option D, 2/3, does not emerge from the simple fraction 2/4 and would incorrectly suggest that only three outcomes are being considered. It cannot be justified from the enumerated sample space.