Grab Bag Probability Question

Derpasaurus

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Jun 16, 2016
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So, I keep messing up on figuring out the chances to win in a grab bag type raffle.

2000 total random bags.
150 random lets say are "winners".
You get 2 random bags.

150/2000 = .075
150/1850 = 1/12.33~ or 12.33:1 odds that your bag will suck?
2/2000 = .001

I keep having a brain fart at this point. What are the chances that one or both of the 2 random bags will be in the 150 "winners"? Thanks for any help on this.
 
2000 total random bags.
150 random lets say are "winners".
You get 2 random bags.

150/2000 = .075
150/1850 = 1/12.33~ or 12.33:1 odds that your bag will suck?
2/2000 = .001
What was the reasoning behind the above computations? What, exactly, are you doing here?

Please be complete. Thank you! ;)
 
So, I keep messing up on figuring out the chances to win in a grab bag type raffle.
2000 total random bags.
150 random lets say are "winners".
You get 2 random bags.

150/2000 = .075
150/1850 = 1/12.33~ or 12.33:1 odds that your bag will suck?
2/2000 = .001
I would none of the above.
There there are \(\displaystyle \dbinom{2000}{2}\) ways to receive two bags.
There there are \(\displaystyle \dbinom{1850}{2}\) ways to receive two bags neither are winner.
How many ways are there to receive two bags where at least one is a winner?
 
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