Probability Question(s)

(I knew I shouldive stayed awake in statistics class)

Let's say your school was holding a lottery, and the winner would recieve $100. The chances of winning the lottery with 1 ticket is only 1/50, BUT: What are the odds of winning if you use like 20 tickets?

1-(49/50)^20

so 0.3324, or around 1/3.

Depends on the number of tickets (>>2 assumes infinite). If there's only one winner, that implies there are 50 tickets, and getting 20 tickets makes your chances of winning 20/50.

What about N tickets?

Well if there's only one winner, then the answer is (no. of tickets you buy)/N.

>>5
That doesn't make sense because winning an N ticket lottery with 1 ticket is 1/50 chance. Winning an N ticket lottery with n tickets is more complicated...I am not sure there is an answer.

>>6
http://en.wikipedia.org/wiki/Hypergeometric_distribution

This especially: http://upload.wikimedia.org/math/d/9/0/d900c57f61cf66ee1be517471f915c8c.png
D = winning tickets
N = number of tickets (50*D in this case)
n = tickets bought
k = desired number of wins
Eg. if there are 2 winning tickets, you need to evaluate the formula for both k=1 and k=2 and sum those two results (since you don't care whether you only win one or both prizes).

>>7
Interesting even though i don't understand it at all.. When i said that there might not be an answer, I was thinking that the probability of a ticket winning is not the same as another ticket winning.

>>6
If there are N tickets and there is one winner who is drawn at random, then 1/50 doesn't come into it.

This is the OR principle.  Your first ticket could win OR your second could win OR your third, etc.  You add the separate probabilities with OR.  With fractions, the numerator is the number of tickets you bought, and the denominator is the total number of tickets in play.

If you are using lottery numbers, then the numerator is the total number of unique combinations you played and the denominator is the total number of number combinations possible according to how the lottery is set up.  For example if the lottery has you choose 6 numbers out of 49, then there are 49C6 combinations (look up the formula or use a scientific calculator with a nCr button) which is nearly 14 million.

>>10
no. The OR principle only works if the events are mutually exclusive: the question is if one of the tickets wins, but the way the problem is specified the person could buy two tickets with the same winning no. - thus making the events not mutually exclusive. thus >>2 is right.

This problem needs to be defined better for us to get the right answer.

>>11
Well the problem appeared to me that whovever operated the lottery of 50 tickets would have the sense to make only one winning ticket, that is to say, 50 unique tickets.  I wouldn't assume that some dumbass created a lottery with 50 tickets to buy that could all win at the same time.

>>11 Anyway, in the case of lotteries like the national lotteries where you could play the same numbers more than once, I see where >>2 makes sense (binomial probability and P(at least one win) = 1 - P(zero win)), so I'm not really disagreeing here.  It just seems weird to me that a guy would run a small lottery like that.