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

LeBron Asks: What are the chances of making 10 free throws in a row?: LeBron James asks Sal how to determine the probability of making 10 free throws in a row

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.  

Sample Space, Clothing and Outfits

Normally a discussion on probability or statistics begins with outcomes from an experiment, what we refer to as sample space


Taken From CNX.org

A sample space is a set or collection of outcome of a particular random experiment.
For example, imagine a dart board. You are trying to find the probability of getting a bullseye. The dart board is the sample space. The probability of a dart hitting the dart board is 1.0. For another example, imagine rolling a six sided die. The sample space is {1, 2, 3, 4, 5, 6}.

Examples of Sample Space.

• The tossing of a coin, sample space is {Heads, Tails}
• The roll of a die, sample space is {1, 2, 3, 4, 5, 6}
• The selection of a numbered ball (1-50) in an urn, sample space is {1, 2, 3, 4, 5, ...., 50}
• Percentage of calls dropped due to errors over a particular time period, sample space is {2%, 14%, 23%, ......}
• The time difference between two messages arriving at a message centre, sample space is {0, ...., infinity}
• The time difference between two different voice calls over a particular network, sample space is {0, ...., infinity}

Many educators use a tree diagram to help students understand outcomes which is a very handy tool. 

(Flipping a Coin and Rolling A Die)

Yet, even with a great tool like a tree diagram, there is still a disconnect between the teaching and the student. We need a better way to reach them!

I like this idea suggested by one of my statistics students!

How Many Outfits Can I Wear?

Using stickers of different clothing (shoes, hats, dresses, etc), let your students discover the amount of mixing and matching they can perform to create different outfits.