Probability vs. Odds, Explained
Date: 03/21/2002 at 21:22:50 From: Brett Subject: Odds in favor There is one coin with heads on one side and tails on the other. We have to find out the odds in favor of getting heads and the odds against. I think the odds in favor and against are the same, 1 out of 2 times, but my teacher said the odds in favor are 1 out of 1. I don't understand. Could you please explain this to me?
Date: 03/21/2002 at 23:15:56 From: Doctor Twe Subject: Re: Odds in favor Hi Brett - thanks for writing to Dr. Math. Let me clarify the difference between probability and odds. The probability of an event is defined as: (Chances for) P(x) = --------------- (Total chances) So, for example, the probability of drawing an ace in a single deck of 52 cards is 4/52 = 1/13 (or about 0.077 = 7.7%). Odds, on the other hand, are given as: (Chances for) : (Chances against) Incidentally, odds of 1:1 would be read as "one TO one", not "one OUT OF one." (The words "out of" seem to imply total chances, which is probability, not odds.) Since (Total chances) = (Chances for) + (Chances against), we can calculate (Chances against) = (Total chances) - (Chances for). The odds of drawing an ace in a deck of cards is 4:(52-4) = 4:48 = 1:12. Notice the difference in the second value; probability uses (Total chances), but odds use (Chances against). This is why the probability (if considered as a ratio) and the odds are different. I hope this helps! If you have any more questions, write back! - Doctor TWE, The Math Forum http://mathforum.com/dr.math/
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