Question: Ms. Ella Brum walks back and forth between her home and her office every day. She owns three umbrellas, which are distributed over two umbrella
- Ms. Ella Brum walks back and forth between her home and her office every day. She owns three umbrellas, which are distributed over two umbrella stands (one at home and one at work). When it is not raining, Ms. Brum walks without an umbrella. When it is raining, she takes one umbrella from the stand at the place of her departure, provided there is one available. Suppose that the probability that it is raining at the time of any departure isp. LetXndenote the number of umbrellas available at the place where Ella arrives after walk numbern;n= 1,2,...,including the one that she possibly brings with her. Calculate the limiting probability that it rains and no umbrella is available.
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