Hi! I am trying to figure out why the answer to the following question is **1/900,000**:

**"What is the probability of guessing my seven-digit number in ten attempts (assume a positive number that's regenerated after each guess, and no leading zero)?"**

How do I go about doing this problem?

WillyGolden Nov 27, 2020

#1**0 **

9 999 999 - 1 000 000 +1 = 9 000 000 seven digit numbers

ten guesses

10 / 9 000 000 = 1 / 900 000

Guest Nov 27, 2020

#2**0 **

So I guess my follow up would be why do we start with "9 999 999 - 1 000 000 +1 = 9 000 000" to get the denominator? My guess is that you subtract the highest possible 7 digit number from the lowest, and then add one. But, I'm not sure why you add "1." Thank you for your help so far!

WillyGolden
Nov 27, 2020

#3**+2 **

The probability of getting the first digit right in one try is 1/9 (because there are only 9 possibilities, since we can't have a leading zero).

The probability of getting the second digit right, having got the first one right is (1/9)*(1/10)

The probability of getting the third digit right, having got the first two right is (1/9)*(1/10)^{2}

...

...

The probability of getting the seventh digit right, having got the first six right is (1/9)*(1/10)^{6}

If you have ten independent attempts then the probability is 10*(1/9)*(1/10)^{6} or (1/9)*(1/10)^{5} or 1/900,000

Alan Nov 27, 2020