The Odds of Confusing Probability with Odds

Or should I say the probability of confusing odds with probability?

Either way, it is very important to note that odds and probability have some major differences.

Lets first review the equations for finding probability (P) and odds (O):

(P) =   # of desirable outcomes                (O) =   # of desirable outcomes  

           # of possible outcomes                         # of undesirable outcomes

I encourage you to look at these equations analytically for a moment and try to imagine how you might change probability to odds and vise-versa using your prior algebraic knowledge. If you are able to figure it out on your own, GREAT! I always retain information better if I am able to solve the problem on my own. I guarantee that you will remember your own thought processes better than you remember my instructions, so please take a moment and just THINK! :)

If you were unable to figure it out on your own, please read on. Even if you think you have the solution, it may be best to also read on in order to gain a better understanding.

Here's an example (you know I love EXAMPLES!):

If you enter into a raffle, would you rather the probability of winning be 49/100 or the odds of winning be 49 : 100?

In order to figure this out, you need to first know how to convert probability to odds and/or odds to probability.

Easy peasy, lemon squeezy!

Converting probability to odds:

- subtract the numerator (# on top) from the denominator (# on bottom) to determine the # of unfavorable outcomes:

P =   49    

       100

100 (# of poss. outcomes) - 49 (# of favorable outcomes) = 51 (# of unfavorable outcomes)

Since you now know the # of unfavorable options, you can figure out the odds:

49 : 51

Converting odds to probability:

- add both sides of the ratio to determine the denominator.

O = 49 : 100

49 + 100 = 149 (new denominator)

So, P = # of favorable outcomes

                          149

Based on the information that you already know, the first # in a ratio shows that # of favorable outcomes.

So..............

P =   49  

       149

Now that you have made your conversions, let's return to our original question:

If you enter into a raffle, would you rather the probability of winning be 49/100 or the odds of winning be 49 : 100?

I prefer to use probability, so here is what we are comparing:

P =    49            OR            P =    49    (O = 49:100)

        100                                     149

Which would to prefer? If you're still not sure, divide for a percentage:

49/100 = 49%         49/100 = 33% 

I'm going with the first one! :)

I hope that this post has helped to illustrate the difference between odds and probability. For further exlantation, visit the following web address: http://www.math-magic.com/probability/prob_to_odds.htm.

For another fun and interesting explanation and to test your knowledge, check out the video below!  

 Thank you for stopping by! Have a wonderful evening!

~ Tammy