Ok, I have no idea how you came up with 57%. Even if you add 18%+30% (which is not mathematically valid) you'd only get 48%. How in the world did you get 57%?!
The real probability based on the article (according to my calculations) is 34.4%, which is actually much better than I would have guessed.
Here is how I came up with that.
The article states a first time entrepreneur succeeds at an 18% rate. And someone succeeds at a 20% rate given they failed the first time.
P(First Time Success) = .18
P(First Time Failure) = .82
P(Success | First Time Failure) = .20
P(Second Time Success) = P(Success | First Time Failure) x P(First Time Failure) + P(First Time Success)
0.344 = .18 + (.82 * .20)
In words: 18 percent of entrepreneurs will succeed on their first try. 82 percent will fail. Of that 82 percent that failed, if they try again, they will succeed 20 percent of the time. To get a number from the original population of first time attempts you have to multiply the 82 percent who failed by the 20 percent who succeeded on the second try which results in 16.4%. That 16.4% is the percentage of the original population who tried on the first try but did not succeed until the second try. The end result being 34.4% of the original population will be successful on their first or second try.
The real probability based on the article (according to my calculations) is 34.4%, which is actually much better than I would have guessed.
Here is how I came up with that.
The article states a first time entrepreneur succeeds at an 18% rate. And someone succeeds at a 20% rate given they failed the first time.
P(First Time Success) = .18
P(First Time Failure) = .82
P(Success | First Time Failure) = .20
P(Second Time Success) = P(Success | First Time Failure) x P(First Time Failure) + P(First Time Success)
0.344 = .18 + (.82 * .20)
In words: 18 percent of entrepreneurs will succeed on their first try. 82 percent will fail. Of that 82 percent that failed, if they try again, they will succeed 20 percent of the time. To get a number from the original population of first time attempts you have to multiply the 82 percent who failed by the 20 percent who succeeded on the second try which results in 16.4%. That 16.4% is the percentage of the original population who tried on the first try but did not succeed until the second try. The end result being 34.4% of the original population will be successful on their first or second try.
Hopefully that makes sense.
* edit to format the formulas a little better