Probability
# Complements

Three integers are chosen at random without replacement from the first 20 positive integers.

What is the probability that their product is even?

Trevor and I were playing golf.

As we all know, Trevor is a pro golfer and I don't know squat about golf (except the fact that we are supposed to hit golf balls with a club).

Now, he made a bet with me. He said, "We will play $N$ matches where you're gonna choose the value of $N$. If you win at least one match, I'll pay you $\$100$ since I'm super rich and if you don't, you'll pay me $\$1$"

Now, I opened my wallet and I saw that it was emptier than a banker's heart. Amongst the cobwebs and flies in it, luckily, there was a $\$1$ bill. Naturally, I accepted the bet since I'm almost broke and need cash.

Generally, if I were to play a match against him, I would have a probability of $0$ of winning. But since here's money involved, the probability of me winning a single match against him is boosted to $\dfrac{1}{3}$.

I want to have at least a $90\%$ chance of winning the bet. What is the minimum value of $N$ that I should choose?