Friday, December 7, 2012

Addressing Our Probability Inefficiencies


The purpose of this activity is short but important. That is to help students NOT associate number of outcomes with probability of outcomes. One could probably teach this to their students faster than they can read this post.

The Problem:

Khan Academy (the wonderful, wonderful people they are) was asked by Lebron James what the chances of making 10 free throws in a row? I won't attempt to outdo Sal on this one




But I want to draw attention to what I find to be a more interesting problem. That is, why do students tend to associate the number of outcomes with the probability of outcomes? In other words, students tend to sometimes think of outcomes such as hit/miss, win/loose, yes/no, etc in terms of each result having a 50/50 chance. Or again, we tend to think that probabilities of outcomes are always distributed equally. This is a dangerous error to make in life, but the good news is that this is often more an academic mistake than a real-life mistake



For example, ask the following two questions to the same person and see what answers you get.

1) If you shoot a basketball, whats the chances of it going in?
2) If you shoot a full court shot, are you more likely to make it or miss it?


The Solution:



The good news is that you can quickly teach kids to be skeptical of this by taking them to a basketball hoop during activity time or gym class and asking the two questions above, then testing them.  

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