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2021 April MIMC 10 Problems/Problem 8

Revision as of 22:04, 20 April 2021 by Cellsecret (talk | contribs) (Created page with "In the morning, Mr.Gavin always uses his alarm to wake him up. The alarm is special. It always rings in a cycle of ten rings. The first ring lasts <math>1</math> second, and e...")
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In the morning, Mr.Gavin always uses his alarm to wake him up. The alarm is special. It always rings in a cycle of ten rings. The first ring lasts $1$ second, and each ring after lasts twice the time than the previous ring. Given that Mr.Gavin has an equal probability of waking up at any time, what is the probability that Mr.Gavin wakes up and end the alarm during the tenth ring?

$\textbf{(A)} ~\frac{511}{1023} \qquad\textbf{(B)} ~\frac{1}{2} \qquad\textbf{(C)} ~\frac{512}{1023} \qquad\textbf{(D)} ~\frac{257}{512} \qquad\textbf{(E)} ~\frac{129}{256}$

Solution

To be Released on April 26th.

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