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 10 cell phones and 10 numbers (Posted on 2008-06-11)
You are given 10 cell phones and 10 cell numbers(each number corresponds to one of each of those 10 cell phones), but you don't know which number corresponds to which cell phone. Your task is to label each cell phone with its corresponding number. Using optimal procedures, what is the probability that you will finish the task in exactly 5 attempts?

A single attempt is defined as calling a number from a cell phone.

Hint: The caller's number will be displayed in the cell that is being called.

 Submitted by Praneeth Rating: 4.2500 (4 votes) Solution: (Hide) Answer: Required Probability = 153,947/201,600 = 0.76363 Explanation: Let S: An attempt from a cell phone calling another cell number. This is Successful attempt. In this case, two cell phones can be labeled. In the best case, 3 cells can be labeled (when 3 cells remain that are to be labeled) Let F: An attempt from a cell phone calling its number. That is Failure. In this case, only one cell can be labeled as we will know that we are calling the same number as the cell phone In the best case, 2 cells can be labeled (when 2 cells remain that are to labeled) The task can be done in 5 attempts if atleast 4 attempts are successful.So, cases in which task can be done: A) S S S S S B) S S S S F C) S S S F S D) S S F S S E) S F S S S F) F S S S S If x cells remain that are to be labeled: P(S) = (x-1)/x P(F) = 1/x P(A)=9/10*7/8*5/6*3/4*1/2 P(B)=9/10*7/8*5/6*3/4*1/2 P(C)=9/10*7/8*5/6*1/4*2/3 P(D)=9/10*7/8*1/6*4/5*2/3 P(E)=9/10*1/8*6/7*4/5*2/3 P(F)=1/10*8/9*6/7*4/5*2/3 So, Probability that the task is done in 5 attempts = P(A)+P(B)+P(C)+P(D)+P(E)+P(F) =153,947/201,600 = 0.76363

 Subject Author Date Nice Solutions Praneeth 2008-06-12 01:59:55 re(5): Solution? Dej Mar 2008-06-11 20:34:04 re(3): Solution? Dej Mar 2008-06-11 20:31:58 re(4): Solution? Charlie 2008-06-11 19:53:25 re(3): Solution? Jyqm 2008-06-11 19:29:07 re(3): Solution? Fernando 2008-06-11 18:20:00 re(2): Solution? Charlie 2008-06-11 18:17:40 re(2): Solution? Josie Faulkner 2008-06-11 18:17:10 re: Solution? Fernando 2008-06-11 18:09:46 Solution? Josie Faulkner 2008-06-11 18:02:03

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