One of the numbers 1 through 10 is randomly chosen. You

Chapter 4, Problem 26P

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QUESTION:

Problem 26P

One of the numbers 1 through 10 is randomly chosen. You are to try to guess the number chosen by asking questions with “yes-no” answers. Compute the expected number of questions you will need to ask in each of the following two cases:

(a) Your ith question is to be “Is it i?” i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

(b) With each question you try to eliminate one-half of the remaining numbers, as nearly as possible.

Questions & Answers

QUESTION:

Problem 26P

One of the numbers 1 through 10 is randomly chosen. You are to try to guess the number chosen by asking questions with “yes-no” answers. Compute the expected number of questions you will need to ask in each of the following two cases:

(a) Your ith question is to be “Is it i?” i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

(b) With each question you try to eliminate one-half of the remaining numbers, as nearly as possible.

ANSWER:

Solution:

Step1 of 2:

      Given the problem, we have one of the numbers 1 through 10 is randomly chosen.

Here we have to compute the expected number of questions you will need to ask in each of the given two cases.

a). Your i th question is to be “Is it i”.

       Here, i = 1,2,3,4,5,6,7,8,9,10.

  Then,

          E( number of questions needed to ask) =  

 

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