How to Multiply Through the Probability Ratio

The probability of being a nice guy is 25 out of 100. To change this into odds, it's the same as saying 25 to 75 or 1 over 3,. Then we can use the likelihood ratio, which is 2.2 and multiply it through. So when you multiply 2.2 likelihood ratio by an odds of 1 to 3, you get 2.2 to 3. Those are the post test odds. Now we have to convert that back into a post test probability. It gets me from 25% to 40%. If I had a test that got me from 25 percent to 90%, now that would be something worth doing. Right?