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To solve this problem, we need to determine which sequence, HHT (Heads-Heads-Tails) or HTT (Heads-Tails-Tails), is more likely to appear first when flipping a fair coin repeatedly. We'll approach this by analyzing the probability of each sequence occurring first.
Initial Conditions:
Breaking Down the Sequences:
Probability of HHT appearing first:
0.5 * 0.5 = 0.25
.0.25 * 0.5 = 0.125
.Probability of HTT appearing first:
0.5 * 0.5 = 0.25
.0.25 * 0.5 = 0.125
.Comparing the Probabilities:
Recursive Probability Analysis:
Final Probability Calculation:
P_HHT
be the probability of HHT appearing first, and P_HTT
be the probability of HTT appearing first.P_HHT + P_HTT = 1
.P_HHT = 2 * P_HTT
.2 * P_HTT + P_HTT = 1
gives P_HTT = 1/3
and P_HHT = 2/3
.The sequence HHT is more likely to appear first than HTT when flipping a fair coin. The probability of HHT appearing first is 2/3, while the probability of HTT appearing first is 1/3. This results from the recursive nature of the sequences and how they reset based on the outcomes of subsequent flips.