Lets say the phone book pages are numbered from 1 - 1000. And assume that the contact is definitely there in the book.

So when you randomly flip open a book there are 1 of 500 choices that it is one one of the two pages that appear before you.

So the probability is 1/500.

Well you can NEVER be 100% sure .... for obvious reasons :)

The 50% is called percent confidence in statistics lingo.

This is best solved by the difference from 1 for the probability of the contact NOT being on the page.

For each attempt to fail we need to multiply 499/500 . So for n attempts to fail it is (499/500)^n. So the probability of it being successful in n attempts is {1-(499/500)^n}

So you need to solve the equation :

{1-(499/500)^n} = .5

which is obviously :

(499/500)^n = .5

And taking log to the base 499/500 on both sides (using python) :

n = 347 attempts

double verify :

So when you randomly flip open a book there are 1 of 500 choices that it is one one of the two pages that appear before you.

So the probability is 1/500.

**Next Question : How many attempts will it take for me to be certain that the contact is there?**Well you can NEVER be 100% sure .... for obvious reasons :)

**Next Question : So how many attempts will it take for me to be 50% sure that the contact is found in one of the two pages that show up?**The 50% is called percent confidence in statistics lingo.

This is best solved by the difference from 1 for the probability of the contact NOT being on the page.

For each attempt to fail we need to multiply 499/500 . So for n attempts to fail it is (499/500)^n. So the probability of it being successful in n attempts is {1-(499/500)^n}

So you need to solve the equation :

{1-(499/500)^n} = .5

which is obviously :

(499/500)^n = .5

And taking log to the base 499/500 on both sides (using python) :

>>> math.log(.5,499/500.0) 346.22690104949118

n = 347 attempts

double verify :

>>> math.pow(499/500.0,346.22690104949118) 0.5