The "odds" are determined by the number of favorable
outcomes to the number of unfavorable outcomes. In the case of flipping a
coin, the odds are 1/1 (sometimes written as 1:1) for heads. The
_probability_ of an event (as per a "frequency" definition) is the number of
favorable outcomes that cause the event to occur to the total number of
outcomes (assuming a uniform distribution). For flipping a coin, the probability
of heads would be 1/2.
Whether or not the total number of tickets sold impacts
your probability of winning depends on the way that the lottery is conducted.
Here in Georgia, I believe that the winning lottery sequence is drawn
from all possile sequences, not from the restricted set of those sequences from
sold tickets only. In the former case, the probability of winning is dependent
only on the number of tickets you purchase. In the latter case (or a similar
case in which winning sequences were generated until someone won), the number of
other tickets sold would affect your chances of winning.
-Nick
Pomponio
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Smith, Jeff
Sent: Friday, October 28, 2005 11:08 AM
To: bob; Tutor@python.org
Subject: Re: [Tutor] Can anyone help me?
But
the odds that you will win are not impacted by the number of tickets that
are sold in total...only the number you buy. When you take into account
the total number of tickets sold, all you get are the odds that the lottery will
be won by anyone.
I'm
also a little confused by that def of odds. Consider flipping a
coin. The probability that it will come up heads is 1/2. That def
says that the odds in favor of it coming up heads is 1.
Jeff
-----Original Message-----At 07:28 AM 10/28/2005, Smith, Jeff wrote:
From: bob [mailto:[EMAIL PROTECTED]
Sent: Friday, October 28, 2005 10:52 AM
To: Smith, Jeff; Tutor@python.org
Subject: Re: [Tutor] Can anyone help me?
Aren't the odds just based on how many tickets you buy? The odds aren't
affected by different people buying more tickets. If only one person
buys a ticket in the entire lottery system, his odds of winning are the
same as if two people play, and the same as if 20 million play.
According to the wikipedia: "In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1-p), where p is the probability of the event or proposition." If you assign equal probability of winning to each ticket then odds are how many tickets you buy relative to how many tickets everyone else has bought.
The probability of a ticket winning is 1 / m**n where m is the highest number possible and n is the number of numbers. If a lottery uses 6 numbers each in the range 1..42 then the probability of a ticket winning is 1/5489031744.
All of this is mathematics. Sometimes one or more tickets win. Is that "luck"?
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