The pot contains 10 counters which are being randomly removed and replaced. How many of each colour do you think are in the pot?
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[Notes for Teacher: The film will go on for ever! It shows a red, green or blue counter being taken from the pot by random selection but in proportion to the number of red, green and blue counters in the pot. Students might make a tally chart to see the relative numbers of counters being pulled out of the pot then divide 10 in the same ratio.]
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Numbers and the Making of Us
I initially heard this book described on the Grammar Girl podcast and immediately went to find out more about it. I now have it on my Christmas present wish list and am looking forward to receiving a copy (hint!).
"Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists." more...
Teacher, do your students have
access to computers?
Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to a student probability activity.
Change the number of counters in the pot:
You can vary the speed of the animation by sliding the handle below to the left or to the right.
We ask for the probability that a number, integer or fractional, commensurable or incommensurable, randomly chosen between 0 and 100, is greater than 50. The answer seems evident: the number of favourable cases is half the number of possible cases. The probability is 1/2.
Instead of the number, however, we can choose its square. If the number is between 50 and 100, its square will be between 2,500 and 10,000.
The probability that a randomly chosen number between 0 and 10,000 is greater than 2,500 seems evident: the number of favourable cases is three quarters of the number of possible cases. The probability is 3/4.
The two problems are identical. Why are the two answers different?
Joseph Bertrand, Calcul des probabilités, 1889 (translation by Sorin Bangu) presented by Futility Closet.