Expected number of coin flips to get two consecutive heads

Analyze the expected number of coin flips to get two consecutive heads.

Difficulty

medium

Companies

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Topic

Mathprobability

Examples

Input: "test_input_1"

Output: "output_1"

Input: "test_input_2"

Output: "output_2"

Hints

Consider using states to model the problem, where each state represents the number of consecutive heads obtained so far.

Let E₀ be the expected number of flips starting from 0 consecutive heads, and E₁ be the expected number starting from 1 consecutive head. Set up equations relating E₀ and E₁ based on possible outcomes of the next flip.

Solve the system of equations derived from the state transitions to find the expected number of flips starting from 0 consecutive heads.

Expected number of coin flips to get two consecutive heads

Analyze the expected number of coin flips to get two consecutive heads.