What is the probability that a randomly selected 2 digit number is prime?

Question

anonymous · Answer

Please explain that please....

anonymous · Answer

Wait, nevermind, that's co-primality, the density of primes is
$$
\pi(x)\sim \frac{\ln x}{x}
$$

anonymous · Answer

I don't understand this

hartnn · Answer

First u need to find how many two digit prime numbers are there.(say x)
Total 2 digit numbers=90,right?
so your probability=x/90
make sense?

anonymous · Answer

2/90?

anonymous · Answer

It's not right, that answer isn't there in my multiple choice sheet

hartnn · Answer

no! there are many prime numbers of 2 digits,not only 2...

anonymous · Answer

Yeah, this proof is absolutely ridiculous, but, if we write a quick computer program to solve it for us (the only human way I see of being able to do this nicely), we get 23.33%

anonymous · Answer

Which is the total number of primes that are two digits over the total amount of two-digit numbers. As @hartnn stated.

anonymous · Answer

Since there are 21 two-digit primes.

anonymous · Answer

Oops there are about 20 prime numbers

anonymous · Answer

OKAY I GOT THE ANSWER NOW

anonymous · Answer

:D 7/30 right?

hartnn · Answer

yup :)

anonymous · Answer

But aren't there from only 99-10 two digit numbers? So how is it over 90?

anonymous · Answer

There are 99-10+1 two-digit numbers (remember 10 is also two digits!)