Problem 19 in Bertsekas “Introduction to Probability”, 2nd ed, page 123.  A prize is randomly placed in one of ten boxes, numbered 1 to 10.  You search for the prize by asking yes-no questions.  Find the expected number of questions until you are sure about the location of the prize, if you ask questions of the form “is it in box k?”  the author provides an answer but not a complete explanation.  Can you please explain how the answer is obtained?

A prize is randomly placed in one of ten boxes, numbered from 1 to 10. You search for the prizeby asking yes-no questions. Find the expected number of questions until you are sure about the…