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# Complements

You are in the complement of the set of people who are not Brilliant.

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

What is the probability that their product is even?

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?

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