## Problem of the Day #342: The Lightbulb
*February 24, 2012*

*Posted by Saketh in : potd , trackback*

A room contains a single light controlled by a wall switch. Initially, it is either turned on or off. Then, $10$ people pass through the room one by one, each with a $\frac{1}{5}$ chance of deciding to flip the switch.

Finally, Muthu enters the room and sees that the lightbulb is turned on. Determine the probability that the light was initially on.

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