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## Telephoney

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #10817 Fun: (2.19) Difficulty: (2.28) Category: Probability Submitted By: mad-ade Corrected By: Winner4600

One boring, rainy Madadian evening, Mad Ade sat waiting for the "Sweaty Chef Kebab" shop to open. He was staring aimlessly at the telephone. He began to wonder to himself, "If you were to dial any 7 digits on a telephone in random order, what is the probability that you will dial your own phone number?"

Assume that your telephone number is 7 digits.

The answer is 1 in 9,000,000.

To my knowledge it is only dialing codes that can start with a zero. As the number is only 7 digits long let's assume no dialing code is present.

The first digit of the number is therefore 1-9.

The 2nd to 7th digit of the number could be 0-9.

Therefore the solution is:

1/9 * 1/10 * 1/10 * 1/10 * 1/10 * 1/10 * 1/10 = 1/9,000,000.

If the first digit can be a zero, the answer would be 1 in 10,000,000.

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