The following is a sequence of content descriptions in the Probability stream (which begins in Year 3).

**Year 3**

*conduct repeated chance experiments; identify and describe possible outcomes, record the results, recognise and discuss the variation* (AC9M3P02)

**Year 4**

*conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results* (AC9M4P02)

**Year 5**

*conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results ; use frequency to compare outcomes and estimate their likelihoods* (AC9M5P02)

**Year 6**

*conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials* (AC9M6P02)

**Year 7**

*conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences* (AC9M7P02)

**Year 8**

*conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results* (AC9M8P03)

**Year 9**

*design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results* (AC9M9P03)

**Year 10**

*design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results* (AC9M10P02)

Looking at the Yr 10 content description and ‘elaborations’, what makes me most angry is that everything is simulation. There is no mention anywhere of any sort of theoretical analysis. I haven’t even bothered looking more closely at the other year levels.

It also said somewhere to explore conditional probability using Venn diagrams and Karnaugh tables. No mention of tree diagrams – which I think are the most natural ‘visual’ representations for this idea.

There’s trees in one Year 10 elaboration, and in two Year 8 and Year 9 content thingos.

Yeah, I know. And that’s fine. My point is that Karnaugh tables and Venn diagrams are explicitly mentioned in the conditional probability elaboration but trees – the natural representation for conditional probability – are .

I see.

No joke about not being able to see the probability for the trees…?

It’s more a matter of not being able to see the trees for the probability …

I have found life tables to be a natural way to intoduse conditional probability even to Year 8 students; see an attached lesson.

s2-ext-lesson18

Terry, there is an edit button for a comment, which stays live for half an hour. You don’t have to delete the comment and start again (and it’s preferable not to don’t).

I wanted to replace the attachment but could not see how to do that.

Ah, I see. Maybe that can’t be done by you. You can always ask me, even after the 30 minutes.

No mention of independence.

You mean in the entire curriculum, or in this thread of contents?

Just this thread

I guess you could call this sampling without replacement.

Indeed. Initially my title was along those lines.

Applied probability: https://www.youtube.com/watch?v=LV2QT41Qrfk

I’m happy to watch an old Dragnet, but where in the epsiode?

It starts at about 3:00

Thanks, it was fun to watch.

Two more interesting points about the Dragnet scene.

First, there is no mention of independence. This is a common error in such arguments. I once heard a statistician criticising an argument about the safety of nuclear power plants. The argument went like this. For a total meltdown, A, B, C, et cetera have to happen. The probability of each of these had been carefully estimated and the probabilities were small. When you multiply all the probabilities together you get an extremely small number. This, in terms of probability, nuclear power plants are quite safe.

I have used a similar example in the past with students in discussing the probability of a house being *totally* destroyed by fire. You need the kitchen, living room, bedrooms, … all destroyed by fire; you can guess the rest of the argument.

Second, at one point in the Dragnet clip, the jury looks quite bored by the mathematical argument. I once heard a statistician telling us about his experience in explaining something similar to a jury in Australia. He had even asked for a blackboard to illustrate the argument. The newspaper reported it as “mumbo-jumbo” the next day.

Yeah that occurred to me, too. The clip works a little differently than intended, or at least is left unexplained. Great clip.

I had a friend who was scared of flying. They always worried that there could be a bomb on the plane. So they always took a bomb with them. They figured that the probability of two bombs on the plane was so small ….

Boom boom.

Thanks Terry, I have a simple mind, so I quite enjoyed the ominous brass motif after the witness said “that’s more people than have ever lived on Earth”.

Coin tossing: https://www.youtube.com/watch?v=gOwLEVQGbrM

Yeah, that’s a great one.