Discrete Mathematics
# Complements

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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