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problem

Starting with an empty string, we create a string by repeatedly appending one of the letters H,M,TH, M, T with probabilities 14,12,14\frac{1}{4}, \frac{1}{2}, \frac{1}{4}, respectively, until the letter MM appears twice consecutively. What is the expected value of the length of the resulting string?
Plain-text mathematical notation (without MathML)
Starting with an empty string, we create a string by repeatedly appending one of the letters H,M,T with probabilities (1)/(4),(1)/(2),(1)/(4), respectively, until the letter M appears twice consecutively. What is the expected value of the length of the resulting string?
Original LaTeX notation
Starting with an empty string, we create a string by repeatedly appending one of the letters $H, M, T$ with probabilities $\frac{1}{4}, \frac{1}{2}, \frac{1}{4}$, respectively, until the letter $M$ appears twice consecutively. What is the expected value of the length of the resulting string?

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Source and history

task_id
339d4ccb-79f1-51e0-925c-94e47524c37f
task_key
test--339d4ccb-79f1-51e0-925c-94e47524c37f
task_revision_id
1
config / split
/ test

Official source

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