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My phone is 2543663 (Posted on 2014-04-15) Difficulty: 2 of 5

I repeat rolling a fair die and writing the result down, - after a while I let the software to continue random generation of the integers 1 to 6 till the 1000th digit.

What is the probability for my 7-digit phone number being somewhere within the sequence?

See The Solution Submitted by Ady TZIDON    
Rating: 3.5000 (2 votes)

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Solution Not likely (spoiler) | Comment 2 of 5 |
There are 994 possible positions to consider.

The probability that it is in any specific one of them is (1/6)^7 = .00000357224

The probability that it is not in any specific one of them is 1-.00000357224 = .99999642776

The probability that it is in none of them is (.99999642776)^994 = .996455

The probability that it is somewhere within the sequence is 1-.996455 = .003545

This is approximate.

The full exact answer, I think, is 1-(1-(1/6)^7)^994

  Posted by Steve Herman on 2014-04-15 12:56:20
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