Greetings Smart people:

I need to know the odds and probability for the below scenario.

Lets say there was a competition.

In this competition there were 300 contestants.

The 300 contestants are competing for 1 of 10 prizes.

First Place: $1,000,000
Second Place: $250,000
Third Place: $100,000
Fourth Place: $10,000
Fifth Place: $10,000
Sixth Place: $10,000
Seventh Place: $10,000
Eight Place: $10,000
Ninth Place: $10,000
Tenth Place: $10,000

My questions:

What are the odds of winning anything at all?
What are the odds of loosing totally?

What are the odds of winning first?
What are the odds of winning second?
What are the odds of winning third?
What are the odds of winning fourth?
What are the odds of winning fifth?
What are the odds of winning sixth?
What are the odds of winning seventh?
What are the odds of winning eighth?
What are the odds of winning ninth?
What are the odds of winning tenth?

What are the odds of finishing in the top three?
What are the odds of finishing in the 4th through 10th category?

I think that is enough for now... Please note that I am aware that
there is a difference between "odds" and "probability" but I do not
know what that difference is. So if you could fill me in on that too I
would really appreciate it.

Hello un5tab1e,

Assuming that all of the 300 contestants have an equal chance of
winning a prize, here are the answers.  (In these answers, I use equal
signs to indicate that one way of expressing the odds is equivalent to
the other ways.)

What are the odds of winning anything at all?  10/290 = 1/29 =
approximately 0.034 = 29 to 1 against
What are the odds of losing totally?  290/10 = 29 = 29 to 1 in favor

What are the odds of winning first?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning second?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning third?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning fourth?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning fifth?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning sixth?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning seventh?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning eighth?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning ninth?  1/299 = approximately 0.00334 =
299 to 1 against
What are the odds of winning tenth?  1/299 = approximately 0.00334 =
299 to 1 against

What are the odds of finishing in the top three?  3/297 = 1/99 =
approximately 0.0101 = 99 to 1 against
What are the odds of finishing in the 4th through 10th category? 
7/293 = 1/59 = approximately 0.0239 = 293 to 7 against

The technical meaning of odds in relation to probability is explained here:

"Odds" [in Wikipedia section]
Answers.com
http://www.answers.com/odds

With regard to your first question, there are 10 chances in 300 that a
particular contestant will win anything at all.  Thus, the probability
of that occurrence is 10/300.  That probability is the numerator for
the odds formula of probability / (1 - probability).  The denominator
for the odds formula is 1 -10/300, which can be expressed as 300/300 -
10/300, or in other words 290/300.  Accordingly, probability / (1 -
probability) for this event is 10/300 / 290/300, or more simply,
10/290.

The odds formula can be used in the same manner for the other
questions you have asked.

Please let me know if you need any clarification.

- justaskscott


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