Question: Rose and Jack plan to study together for the Math test. They decide to meet at the library between 8:00pm and 8:30pm. Assume that they

Rose and Jack plan to study together for the Math test. They decide to meet at the library between 8:00pm and 8:30pm. Assume that they each arrive (independently) at a random time (uniformly) in this interval. It is possible that someone has to wait up to 30 minutes for the other to arrive.

(a). What is the probability that someone (Rose or Jack, whichever arrives ﬁrst) must wait more than 20 minutes until the other one arrives? What is the probability that Joe waits more than 20 minutes?

(b). What is the expected amount of time that somebody (the ﬁrst person to arrive) waits? Formulate the problem and solve. Make sure you carefully deﬁne the random variables you use!

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