In this lesson for statistics help, we will discuss a problem in statistics while giving four helpful ways for students to improve in their statistical analysis.

Our first example questions is thus:
There are 12 horses competing in a race.  What is the probability two of them owned by one person finishes first and second?  Lets assume none of the horses can tie.

This brings us to my first helpful tip for solving a statistics question:
Don’t think too deep into the question, just think, “what is this problem asking of me?”

For this example the first thing I would do is give the question two full attention reads.
I understand after two reads that we need to find the probability using the definition of classical probability.  In this case we want to know the percentage chance that the two horses finish first and second without regarding the order.  There can only be 2 favorable outcomes, one comes in first and the other in second and visa versa. 

Next helpful hint for solving a statistics question is to always have the equations on hand and prepared.  Write the equation before you start trying to solve it.  Writing it will prevent mishaps or any mistakes when setting up your solution.

Back to our example we see that our equation can only be

P(E) = Number of outcomes in event E / Total number of outcomes in sample space

Because success is not affected by the order of the given two horses, the total number of outcomes is the number of combinations of 2 horses selected from all 12.

For additional statistics help, I head into my third tip.  Always fill in every variable with your numbers and do not try to solve any before writing them, doing so you may make a mistake when trying to solve the algebraic part of the equation.

So we set up our problem like so:

 C = 12! / [(12-2)! 2!]
Simplifying this gives us
 C = 12! / 10! 2!
 C = 66

Now this is where most people would stop.   Which leads me to the final tip for solving your statistics problems.

Always make sure you FINISH the problem and don’t think just because you came up with a equation and solved it the problem is over.

This problem is a perfect example of how easy it is to think a problem is solved when its not quite there. We have to continue to solve the problem by using the classical probability formula to find the % chance that the given two horses finish.

P = 1 / C
p = 1/ 66
p = .0152

Thus, the probability that two horses owned by one person finish first and second is approximately .0152. 

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