There's a raffle with 1,000 names in a bucket. 600 of those names are in there once, and 200 are in there twice. So, just to reiterate, there are 800 unique names in the raffle, and 1000 names total. 500/1000 names will be selected from the raffle.
Q1: What is the probability of being selected if your name is in the bucket
once?
Q2: What is the probability of being selected if your name is in the bucket twice?
The answers are:
Q1: 500/100 = 50% chance of being drawn if your name is in the bucket once
Q2: 500/1000 + (500/1000)*(499/999) = 75% chance of being drawn if your name is in the bucket twice.
How do these answers make sense? Is there another way of arriving at these answers? I can't seem to understand these conceptually. Thank you!
Best Answer
Q1 is pretty easy. You have one ticket in there, they draw half of them out, so you have a 50% chance.
Q2 is more interesting. You can see it as $1-$ the probability of you not getting picked after 500 times, which is $1-\frac{998}{1000}*\frac{997}{999}*...*\frac{498}{500}=1-\prod_{k=1}^{500}\frac{998-k}{1000-k}=1-.249249249...\approx.75$.