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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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.