Probability of At Least One Head – UGC NET Question

When three fair coins are tossed, there are 2³ = 8 equally likely outcomes. The easiest way to find the probability of at least one head is to subtract the probability of getting no heads (i.e., all tails) from 1. The probability of all tails is 1 outcome (TTT) out of 8, which is 1/8. Therefore, the probability of at least one head is 1 − 1/8 = 7/8.

Option A:
Option A, 1/8, gives the probability of the complementary event (no head) rather than at least one head. It represents the chance of all tails.

Option B:
Option B, 3/8, might come from counting only single-head outcomes and ignoring cases with two or three heads, so it underestimates the event.

Option C:
Option C, 5/8, still misses some favourable outcomes and does not match the simple complement calculation.

Option D:
Option D correctly uses the complement rule and recognizes that all outcomes except the single all-tail result satisfy “at least one head,” leading to 7/8.