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update problem 3 contemporary
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allardjun committed Apr 10, 2024
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%%%%%%%%%%%%%% PROBLEM %%%%%%%%%%%%%%%%%%
%\item
Thanks to social distancing and vaccine rollout, UCI has entered Phase III Research, and biologists are allowed back in their labs.
%Thanks to social distancing and vaccine rollout, UCI has entered Phase III Research, and biologists are allowed back in their labs.

In the old days, it used to rain in California.
%In the old days, it used to rain in California.

Suppose a biologist possesses $4$ umbrellas which he employs in going from his home to his lab and vice versa. If he is at home (lab) at the beginning (end) of his day and it is raining, then he will take an umbrella with him to the lab (home), provided there is one to be taken. If it is not raining, then he never takes an umbrella. Assume that, independent of the past, it rains at the beginning (end) of a day with probability $p=0.1$.

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