If you flip a coin three times, what is the probability of getting exactly two heads?

Instruction: Assume three independent tosses of a fair coin. List the sequences with exactly two heads and calculate their total probability.

Context: This question evaluates the candidate's grasp of combinations and basic probability calculations.

Updated

Official answer

For three independent fair tosses, the eight ordered sequences are equally likely. Exactly two heads occur in HHT, HTH and THH, so the probability is 3/8 = 37.5%.

Equivalently, choose which two of the three positions contain heads: C(3,2) × (1/2)^3 = 3/8. HTT, THT and TTH each contain only one head and do not belong in this event. For independent tosses with head probability p, the corresponding answer is 3p²(1−p).

Related Questions