Quote:
There are 100 tickets available for a raffle. If I buy one ticket, my odds are 1 in 100. If I buy 5 tickets do my odds become 1 in 20?
Yes.
If you want confidence in your calcs then it's always good to come to the same result using two different approaches. One you already have. The other is this way:
In probabilty it's almost always better to think about the question from the other side. i.e.:
"What are my chances to win within 5 draws"
becomes
"What are my chances
not to lose with 5 draws"
The other consideration is: All probabilities for all possible outcomes always have to add up to 1. So
"chance to win within 5 draws" + "chance to lose with 5 draws" = 1
or
"chance to win within 5 draws" = 1 - "chance to lose with 5 draws"
So all we have to figure out is what the probability for "chance to lose with 5 draws" is.
Chance to lose on draw 1: 99/100
Chance to lose on draw 2: 98/99 (since one ticket is now already gone we have to divide by 99 not 100)
Chance to lose on draw 3: 97/98
etc.
Plug that into the equation and it looks like this:
"chance to win within 5 draws" = 1 - (99/100 * 98/99 * 97/98 * 96/97 * 95/96)
Plug into calculator and you get
"chance to win within 5 draws" = 5%
Last edited by antialias; 07-11-2018 at 05:40 PM.