This is a problem that I occasionally run into when playing card games. The numbers and variables can change, but the basic idea is always the same. I would like both the answer to the problem below as well as how to solve similar problems in the future.
The problem: I have a deck of 20 cards. I will draw 4 cards from this deck. 2 of the cards are red, and the rest are blue. What are the odds of me drawing at least one red card?
If possible, an exact way to solve as well as a decent "estimate" way to solve it would be useful; the more exact way can be used during deckbuilding, when I can take as long as I need, where the quick way is useful in the middle of a game, and I don't (or can't) take too long to decide what to do.
Thanks in advance to everyone who helps me with this.
You'll have to clarify for me.
I know the odds of rolling X on a die is one in six - six possible outcomes, one of which is good. The bigger issue here comes from multiple drawings. It would be the same as rolling the die 4 times, and seeing the odds of rolling any fours. Also, the denominations in the various fractions are different, so having them interact with each other is hard.
So in this case, the odds of a drawing a red card are 2/20 (1/10) for the first draw, then 2/19 for the second draw, then 2/18 (1/9) for the third, and 2/17 for the last draw.
So the first draw isn't hard, it's a 10% chance. The second draw is obviously better than that, it's about 10 and a half percent chance. The third one is 11%, and the fourth is almost 12% (11.7). What I don't know how to do is...
And the second one in particular is what I need, although both bits are helpful.