### Brain Teasers

# Telephoney

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

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.

Assume that your telephone number is 7 digits.

### Answer

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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## Comments

I think the answer according to the wording is 1 in 10 000 000. The teaser said dial in random order. Like if a monkey started pushing the buttons. The monkey is not going to say hey I had better not push zero first up because that's not a proper phone number!

the answer does say it is 1/10,000,000 if the first number is a zero, and 1/9,000,000 if you only count possible valid phone numbers.

A small technicality for Australian viewers. Here in Oz we have 8 digit phone numbers. Dialing 7 random numbers has 0% probability of getting anyone's phone number at all, least of all your own!!!

and that is why the teaser clearly states "assume that your telephone number is 7 digits"

Easy to figure out but harder to explain why....

If the number could have started with a zero, it would have been 10 to the power of 7 because there would have been 10 digits possible.

Thats why the answer is 100,000,000

Thats why the answer is 100,000,000

Who really cares?

thats wrong because 0 MUST be inclided if the number is random

In the US at least, the 1st number cannot be a 1 or 0 (1 calls long-distance, 0 calls the operator), and the fourth number cannot be 9, as this is reserved for pay phones. There may be other restrictions, but I doubt it.

This isn't about how many possible valid telephone numbers there are; this is about the probability that seven random digits will match a specified phone number. All 10,000,000 of the possible 7-digit numbers are equally likely to result from the randomization process, be they valid phone numbers or not. The given answer is wrong.

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