About Tier 5 - Singularity
The highest challenge tier, usually requiring deep or non-obvious reasoning.
Difficulty describes the challenge, not the solver. It is a Society guide rather than a formal academic level.
The tier is a Society guide to the amount of reasoning, technical work and insight a problem is expected to require. Your experience may vary depending on the topic and your background.
Waiting for Two Heads
Probability / Expected Waiting Time - 15-20 min
Start with no tosses made. Toss a fair coin independently until two consecutive heads appear for the first time, then stop immediately. What is the expected total number of tosses, including the two heads that finish the experiment?
Here 'expected' means the average number of tosses over many repetitions of the complete experiment.
Assumptions
Tosses are independent, and heads and tails each have probability one half. There is no time limit. The expected count is the average over repeated complete experiments, not a guaranteed stopping time.
More Options for Waiting for Two Heads
Collection question · Revision 1 · ID: waiting-two-heads