Expected Probabilities

1. Expected Probabilities Slideshow 50, Mathematics Mr Richard Sasaki, Room 307

2. Understand how expected probabilities are created Use notation to show such expected probabilities Objectives

3. Vocabulary We need to learn or review some vocabulary. The thing that is taking place (eg: Rolling a die) Event - Possible outcomes for the event (for a die: 1, 2, 3, 4, 5, 6) Value - Frequency - The number of times a value appears in an experiment Biased - Unfair. Higher probabilities for some values than others. Fair. All values have equal probabilities. Unbiased -

4. Expected Probabilities If we carry out an experiment for something where we don’t know the probabilities for each occurrence (eg: an unfair die), we can calculate expected probabilities. For these to be anywhere near accurate we would need to do the experiment many, many times. We will use the results to help us understand what the probabilities for each occurrence may be like.

5. Expected Probabilities E(1) E(2) E(3) E(4) E(5) E(6) = = = = = = This is an example result of an unfair die rolled 100 times. We can’t be certain of any probabilities but we can guess from our results. For expected probabilities we use the notation E(Something) where something is the event. (Don’t use P(Something) as these aren’t actual probabilities!)

6. Expected Probabilities We can’t be certain, but it looks like P(4) is much more likely to happen than the others. Note – Accuracy lessens as values get lower. For example, we can’t really say that P(1) would be more likely than P(2) due to chaos. Remember, chaos affects things with lower values more than higher values. Try the short worksheet!

7. Answers • 10 • 4 (Far lower results) • 3 – not confident as the results are similar to values 1 and 2. 2. Tails, 47 b. E(Heads) = , E(Tails) = c. No, this outcome is highly possible with an unbiased coin.