# If an integer is randomly chosen among the first 50 positive integers, what is the probability that the chosen integer will be a 2-digit number?

I thought that this question would simply be that there are 40 2-digit integers so you have a $$\frac{40}{50}$$ chance of getting a 2-digit integer via relative frequency.

However the answer says that it is 0.82, and it doesn’t show any work. Am I thinking about this problem in the wrong way?

• That's because there are forty-one positive integers between $1$ and $50$ inclusive. Sep 29, 2019 at 18:22
• There are only $9$ positive one-digit integers Sep 29, 2019 at 18:24
• I think you meant, Lord Shark, that there are forty-one two-digit positive integers between 1 and 5 inclusive. Sep 29, 2019 at 18:28

The two-digit numbers between $$1$$ and $$50$$ are from $$10$$ to $$50$$ (both included). This amounts to $$41$$ numbers to choose from. Hence probability will be $${41\over 50}$$.