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Understanding Randomness and Probability in Mathematics

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felton
10 diapositives · 242 Views · Jul 18, 2014

This presentation, led by Mr. Richard Sasaki, explores the concepts of randomness and likelihood in mathematics. Students will learn how randomness occurs, the importance of understanding likelihood, and basic notations used in probability. Through interactive activities like flipping a coin multiple times, participants will grasp how human attempts at randomness can often lead to patterns, contrasting with true randomness. The session emphasizes the foundations of probability, helping students articulate their intuition about chance using terms like certain, likely, and impossible.

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  1. Likelihoodand Randomness Slideshow 48, Mathematics Mr Richard Sasaki, Room 307

  2. Objectives Understand how randomness is made possible Understand the concept of how likely something is to happen Understand some basic notation

  3. Something that has no pattern and is not affected by anything. There is no way to make a right or wrong guess. Randomness Any patterns that appear are pure luck or chaos. Outcomes have no reasoning for single tests. What is randomness?

  4. Let’s try a test. Imagine if you flip a coin 30 times. We know “heads” and “tails” have both 50% chance each. Is it random or does it just look random? Can you be random? Omote – 表 Ura – 裏 Heads Tails In the top row, try to guess a random list of heads and tails.

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

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

  7. Probabilities are values to show how likely something is to happen. Probabilities 0 1 0.5 Half chance it will, half it won’t. Will definitely not happen. Will definitely happen.

  8. What is likeliness? Likeliness is how much of a chance you think something will happen. Likeliness Using phrases, we have… Certain = 1 Very Likely 0.5 < < 1 Likely Even chance = 0.5 Unlikely 0 < < 0.5 Very Unlikely Impossible = 0

  9. 0 1 0.5 Unlikely Likely Answers Certain Even Chance Impossible 0 < Uncertain < 1 Unlikely, Likely, Unlikely, Impossible, Certain, Even Chance Unlikely, Very Unlikely, Impossible Example - I will swim to school tomorrow.

  10. The notation for writing “The probability of” is very simple. Notation P(____) So for example “The probability of it snowing tomorrow” could be… P(Snow Tomorrow)