Three unbiased coins are tossed. What is the probability of getting at most 2…

When a fair coin is tossed n times, each of the 2n possible outcomes (sequences of heads and tails) is equally likely. The classical probability of an event is the number of favourable outcomes divided by the total number of outcomes; when the complementary event is easier to count, P(event) = 1 − P(event does not happen).

For 3 tosses, the total number of outcomes is 23 = 8.

• 0 heads: 1 outcome (TTT)

• 1 head: 3 outcomes (HTT, THT, TTH)

• 2 heads: 3 outcomes (HHT, HTH, THH)

Adding these gives 1 + 3 + 3 = 7 favourable outcomes out of 8, so the probability of at most 2 heads is 7/8.

Cross-check (complement method): the only outcome that does NOT satisfy “at most 2 heads” is 3 heads (HHH), which is 1 outcome out of 8. So P(at most 2 heads) = 1 − 1/8 = 7/8, confirming the result.