(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

You flip a fair coin until you get the same face twice in a row.

What is the probability that you stop on an even number of tosses?

Example: Probability of taking less than 6 tosses to stop is 15/16

In general, the probability of stopping on the nth toss is 1/2^(n-1)

2. Relevant equations

Example: Probability of taking less than 6 tosses to stop is 15/16

In general, the probability of stopping on the nth toss is 1/2^(n-1)

The sum of probabilities as n (the number of tosses) grows is 1.

3. The attempt at a solution

Pr(2 tosses) = 1/2

Pr(3 tosses) = 1/4

Pr(4 tosses) = 1/8

In general there are only two sequences for n tosses that end on the nth toss.

Either it starts with tails and alternates until the last 2 tosses or it starts with

heads and alternates until the last 2 tosses.

Example

HTHH

THTT

Only 2 sequences that end on the 4th toss.

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# Probability of Same face in Coin flips

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