Please help settle an argument amongst friends. We put 10 names in a hat and are drawing out of the hat twice.
After the first draw we are putting the name drawn back into the hat.
Before any draw what are the odds that your name will be drawn at least 1 time. Is it 20% or is it adjusted down, since the first name drawn is going back into the hat?
Also what are the odds that same person is drawn both times. Thanks
The chance your name is not drawn on a given draw is $0.9$, so the chance it is not drawn in two draws is $0.9^2=0.81$. The chance your name is drawn at least once is $1-0.81=0.19$ or $19\%$. The reduction comes because you have $1\%$ chance of being drawn twice.