An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials: 1. HTHTHT 2. TTHHHT 3. HTTHHT 4. HHHT_ _ Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct? A. Two T will occur. B. One H and one T will occur. C. Two H will occur. D. One H will be followed by one T.

GATE 2018 · General Aptitude · Probability · medium

Answer: The statement with the highest probability is B: One H and one T will occur, with probability 1/2. Answer: B.

1. Recognize independence: past tosses don't matter: The 4 observations (HTHTHT, TTHHHT, HTTHHT, HHHT__) are given to test whether students fall for the gambler's fallacy. For an unbiased coin, P(5th toss = H) = P(5th toss = T) = 1/2.
2. Compute probability of each option: A. Two T: P(TT) = 1/2 * 1/2 = 1/4. B. One H and one T: P(HT or TH) = 1/4 + 1/4 = 1/2. C. Two H: P(HH) = 1/2 * 1/2 = 1/4. D. H followed by T (i.e., HT specifically): P(HT) = 1/4.
3. Identify the highest probability: P(B) = 1/2 is the maximum. Option B (One H and one T will occur) has the highest probability.