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 Probability Discussions of probability theory

 07-11-2018, 12:53 PM #1 Kashtree stranger   Join Date: May 2011 Posts: 5 Please help with this basic probability equation I know its basic and simple but I want to make sure I've got the equation correct. Here's the query... 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? Just need one of you math whiz guys to correct me if I am screwing that up.
 07-11-2018, 01:03 PM #2 whosnext Pooh-Bah     Join Date: Mar 2009 Location: California Posts: 4,853 Re: Please help with this basic probability equation Just to be clear, you are assuming: - only one prize - prize winning ticket is randomly chosen with each ticket having the same chance of being chosen - all 100 tickets are sold Then, clearly, if you buy one ticket the probability of you winning the prize is 1/100. And if you buy 5 tickets the probability of you winning the prize is 5/100 (or 1/20). Are you asking about the semantics of "odds" (the relationship between odds and probabilities)?
07-11-2018, 05:30 PM   #3
antialias
journeyman

Join Date: May 2018
Posts: 217

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.

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