Likelihood and Randomness

Slideshow 48, Mathematics

Mr Richard Sasaki, Room 307

Objectives

• Understand how randomness is made possible

• Understand the concept of how likely something is to happen

• Understand some basic notation

Randomness

What is randomness?

Something that has no pattern and is not affected by anything. There is no way to make a right or wrong guess.

Any patterns that appear are pure luck or chaos. Outcomes have no reasoning for single tests.

Is it random or does it just look random?

Can you be random?

Let’s try a test. Imagine if you flip a coin 30 times. We know “heads” and “tails” have both 50% chance each.

In the top row, try to guess a random list of heads and tails.

Omote – 表Heads

Ura – 裏Tails

Looking good!

Now a coin will be passed out. Flip the coin thirty times and record the results!

I bet your results were pretty different. The coin probably had patterns of the same thing 5 times in a row or maybe even more!But the human trying to be random, won’t let a row of the same go over about three, naturally.

Randomness

Randomness is a hard thing to understand well, mainly because humans aren’t good at doing things randomly.

Things without brains (like coins) are much better at being random!Of course though, it is possible to understand randomness and how likely something is. That is why we have probability!

Probabilities

Probabilities are values to show how likely something is to happen.

0 10.5Will definitely not happen.

Will definitely happen.

Half chance it will, half it won’t.

Likeliness

What is likeliness?

Likeliness is how much of a chance you think something will happen.

Using phrases, we have…Certain

Very LikelyLikely

Even chanceUnlikely

Very UnlikelyImpossible

= 1

0.5 < < 1= 0.5

0 < < 0.5

= 0

Answers

0 10.5

Impossible CertainEven Chance

Unlikely Likely

0 < Uncertain < 1

Unlikely, Likely, Unlikely, Impossible, Certain, Even ChanceUnlikely, Very Unlikely, Impossible

Example - I will swim to school tomorrow.

Notation

The notation for writing “The probability of” is very simple.

P(____)

So for example “The probability of it snowing tomorrow” could be…

P(Snow Tomorrow)