Calculate Expected Flips for Heads-Tails Sequence

Q: Calculate Expected Flips for Heads-Tails Sequence

This question evaluates a candidate's proficiency in probability theory and stochastic-process reasoning, including Markov-style state modeling and expected-value analysis for stopping times.

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Question

Probability Check — Waiting Time for HT

Setup

You repeatedly flip a fair coin (independent flips; P(H)=P(T)=1/2).
Stop as soon as the consecutive pattern HT appears for the first time.

Question

What is the expected total number of flips required until HT first appears?

Hint: Model states as Start (no useful last flip), H (last flip was H), and an absorbing state (HT seen). Set up and solve expected-value equations.

Calculate Expected Flips for Heads-Tails Sequence

Probability Check — Waiting Time for HT

Setup

Question

Solution

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