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January PoTM

Beary the bear is trying to catch her brunch, invisible salmon! She wakes up every day at a random time between 7:30 and 8:00 AM and takes 15 minutes to reach the river. She waits at the river for 20 minutes. If no salmon appear, she leaves, but 10 minutes later she will regret her decision and return to wait for 15 more minutes. If still no fish appear, then she will go back to her den and instead will eat mushrooms. The salmon at the river come at a random time between 7:55 and 8:30 AM, and if they don’t see Beary, they will be visible for 5 minutes. Otherwise, they will stay invisible and leave immediately. What is the probability that Beary eats mushrooms for brunch on a given day?

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Written by Ella Zheng

 

Submit your answers in the Google Form: https://forms.gle/Q8VVyQs5vTNrbVxq8.

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Stuck? Check out these resources and hints:

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  1. Write the times that Beary will get to the river in terms of the time that she wakes up.

  2. Try to think geometrically and compare Beary's time with the salmon's time. Here is a helpful AoPS article: https://artofproblemsolving.com/wiki/index.php?title=Geometric_probability.

  3. What are the conditions that Beary eats mushrooms?

 

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