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jmc

counting and probability junior

Problem

Mr. Patrick is preparing a five-question true-false quiz for his class. He flips a coin before writing the first question. If it is heads, he writes a true statement and if it is tails, he writes a false statement. He continues this until all five statements are written. What is the probability that the correct sequence of answers is TFTFT ? Express your answer as a common fraction.
Solution
Since all sequences of 5 answers are equally likely, the probability of any given 5-answer sequence is simply , since each answer is equally likely to be true or false. So, the answer evaluates to .
Final answer
\frac{1}{32}