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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Texas Instruments Nspire Calculator
This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.
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Apple iPad Pro
The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.
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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.