Explain "equally likely" in continuous uniform distribution using everyday items?

Question

What is the best way to explain "equally likely" in continuous uniform distribution to an audience using tangible or everyday items?

Answer 1

So, this question has two parts:  there's the part about "equally likely," and the part about "continuous." 

Let's say you're visiting Disney, you go park your car, and then you go wait for the tram to take you into the park. Let's say that Disney tells you that a tram is going to come every 10 minutes.  If that's true, and I ask you how long you're going to wait for the next tram, your answer is "I dunno, somewhere between 0 and 10 minutes."  It could be any value between 0 and 10, like 3 minutes and 4 seconds...and if you have a really good stopwatch, you could even measure it to the fraction of a second.

 

That's the "continuous" part.  Any value is possible.  It's not just exactly 1 minute, or exactly 2 minutes...it's anything.

 

Unless I do some special planning, my wait time for the next tram is going to be completely random. There's no reason to believe that I'll wait 1 minute, instead of 3 minutes and 5 seconds, or 9 minutes and 54 seconds.  Any time between 0 and 10 minutes could happen, and any of those times is just as likely as any other.  It's complete luck.

 

That's the "equally likely" part.

 

Hope this helps,

 

Answer 2

When you say "continuous uniform distribution", it implies a range of values or outcomes----i.e. more than 2.  So, the first thing you have to define is the entities, groups, or whatever that are "equally likely"

 

for example, you might be planting wild-flower seeds where you know 2 things:

There are exactly the same number of seeds for each of 3 colors

All seeds have the same probability of germination.

 

From this, you can say that the occurrence of each of the 3 colors is equally likely

 

One classic demonstration is the marbles passed thru a set of pegs forming a Gaussian distribution.  You can show intuitively that marbles are equally likely to land above or below the mean.