Gotham Gets the Math Wrong

There are many current TV series with a comic book/super hero theme, and I watch most of them.  There's Supergirl, Sleepy Hollow, SHIELD, The Flash, Legends of Tomorrow, The Green Arrow, etc.  Another of my favorites is Gotham.  While recently watching one of the episodes I noticed a very basic math mistake.  There's a scene in which The Riddler is trying to determine the odds of Detective Gordon finding the Penguin and then the odds of the Penguin telling Detective Gordon the truth.  Here's my paraphrasing of the conversation The Riddler has with himself.

"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!!!