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.

(In reply to re(2): Solution? by Charlie)

I believe the probability may be more complex. One can call the same cell on any of the first four attempts as long as a second call to a same cell is not made on any of the other attempts.

Chance of calling any of the first four cell phones other than the one dialed is: 9/10 * 7/8 * 5/6 * 3/4 = 63/128.

Chance of calling the same phone as dialed on the first attempt with the probability that the other calls are not to the same dialed cell is: 1/10 * 8/9 * 6/7 * 4/5 * 2/3 = 64/1575.

Chance of calling the same phone as dialed on the second attempt with the probability that the other calls are not to the same dialed cell is: 9/10 * 1/8 * 6/7 * 4/5 * 2/3 = 9/175.

Chance of calling the same phone as dialed on the third attempt with the probability that the other calls are not to the same dialed cell is: 9/10 * 7/8 * 1/6 * 4/5 * 2/3 = 7/100.

Chance of calling the same phone as dialed on the fourth attempt with the probabiliy that the other calls are not to the same dialed cell is: 9/10 * 7/8 * 5/6 * 1/4 * 2/3 = 7/64.

The cumulative probability is, then,
63/128 + 64/1575 + 9/175 + 7/100 + 7/64 =~ 0.763626 chance of successfully identifying all ten cells in five attempts.

Posted by Dej Mar on 2008-06-11 20:31:58