"What are odds Detective Gordon will learn the truth. Let's say the odds of Gordon finding the Penguin are 80% and the odds of the Penguin telling Gordon the truth are 80%. That's a 60% chance Gordon will learn the truth. That's too high for my comfort."
So what's wrong here? I'll be blunt. The odds of Gordon learning the truth are NOT 60%. This is a classic misconception on how statistics work. If there are two odds, you simply do not subtract the difference from 100% to get the answer. Think about it this way, the odds of flipping a coin and getting tails is 50%. What are the odds of flipping a coin twice and getting tails both times? Not an absolute decrease of 50%. If that was the case, the odds would be 0% and that is obviously incorrect. The odds of getting tails twice are 25%. Let's apply this to the Gotham quote.
If the odds of each of the two items is 80%, we can find the odds of both items happening by multiplying the percentages.
Correct Odds = (80%)*(80%)
Correct Odds = (0.8)*(0.8)
Correct Odds = 0.64
Correct Odds = 64%
The correct answer is 64%, not 60%. What's even more wrong with the quote in this episode is that it came from a character who is very smart and stereotyped as the nerd character. This character would NOT make this simple math mistake.
Yeah, I'm being picky. I still love the show, but it sure would be nice if the writers would get the basic math correct!!!