Probability Notes: HK Syllabus & Recommendations

[dalcde]

I have made some study notes on probability. Please have a look and see if there are recommendations. I'm forced to follow the syllabus in Hong Kong so I had to add some boring and nonsense stuff inside (unfortunately).

 

[dmatador]

Proof. By definition, equally likely events have equal
probability of happening. Suppose that the probability is p.
Since we are sure that something will happen, the total
probability of the events is equal to 1. Hence we have
Obviously p=1/n. Hence the probability of each event is
equal to 1/n.

This could stand to be more rigorous. You could simply employ some subscripts for your p's. I know that you have demonstrated that probabilities for all events are the same, but it would benefit a first time reader of material on probability to know that you are talking about partitions of a sample space, which are distinct events with their own probabilities that add up to 1. How you have written it is rather vague.

You could perhaps touch upon the idea of independent events. For instance, you give some examples of throwing dice, or, you could limit yourself to one die for simplicity. Throwing a 1 and then a 6 are two independent events, so the probability of this event is the product of the probabilities of the two events that comprise it.

 

[dalcde]

I'd like to, but this is intended for year 9 (scondary 3) high school students. I want to introduce some rigor but not too much.

 

[dalcde]

Frankly speaking, their primary objective of learning this is to pass exams. I doubt that there would be more than 10 people actually reading the proof.

Thanks for the comment.