Question

Kate has n keys, only one of which will open the cookie jar. (a) If she tries the keys at random, discarding those that do not work, what is the probability that she will open the jar on her kth try? (b) Later in the day, her brother Kurtis wants to get a cookie, but he does not discard keys that he has previously tried. What is the probability that he will open the jar on his kth try? (c) Kurtis forgets to re-lock it, and his sister Caroline finds the open cookie jar Caroline knows that the time until the next person walks into the kitchen follows an exponential distribution with rate A-.95. It takes her 2 minutes to eat the cookie. What is the probability that someone catches her sneaking a cookie? (d) Given that no one has walked in during the two minutes Caroline was eating her first cookie, what is the probability that someone will catch her while she eats her second cookie?

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