Suppose you have four origami books which are labelled B1, ..., B4. The books are kept...

Transcribed Image Text:

Suppose you have four origami books which are labelled B1, ..., B4. The books are kept stacked on your desk. Each day you select one book from the stack and build a model. Books are selected each day at random with probabilities P(B, is selected) = (5 - i)/10 and independently of past selections. At the end of the day you place the selected book on top of the stack. Suppose on day 0 the books are stacked in order of the labels. That is, book Bı is in first position (top), book B2 is second from the top, book B3 is third from the top, and book B4 is on the bottom. (a) What is the probability that book B1 is on top of the stack at the end of day n? Does this probability depend on n? (b) Give an expression for the probability that book B1 is second from the top of the stack at the end of day n. What is the limiting value as n → o ? Suppose you have four origami books which are labelled B1, ..., B4. The books are kept stacked on your desk. Each day you select one book from the stack and build a model. Books are selected each day at random with probabilities P(B, is selected) = (5 - i)/10 and independently of past selections. At the end of the day you place the selected book on top of the stack. Suppose on day 0 the books are stacked in order of the labels. That is, book Bı is in first position (top), book B2 is second from the top, book B3 is third from the top, and book B4 is on the bottom. (a) What is the probability that book B1 is on top of the stack at the end of day n? Does this probability depend on n? (b) Give an expression for the probability that book B1 is second from the top of the stack at the end of day n. What is the limiting value as n → o ?