1. ▲There are more red balls in box A than in box B.
S1.1 Core Plenary
True or false but WHY?
▲There are more red balls in box A than in box B.
If you choose 1 ball from each box at random you are more likely to choose a red ball from A than from B.
▲Janet buys 2 raffle tickets. If she chooses two tickets from
different places in the book she is more likely to win than
if she chooses two tickets next to each other.
▲When six fair dice are thrown at the same time, you are less likely to get 6, 6, 6, 6, 6, 6 than 1, 2, 3, 4, 5, 6 in this order.
A B
Preamble
This activity provides pupils with the opportunity to discuss counter-intuitive probability. It is expected that pupils pursue a qualitative approach rather than calculating any actual probabilities. The activity is suitable for pairs or small groups followed by whole-class discussion, it recaps on the work just completed. Other cases of counter-intuitive probability (for example, 6s are harder to throw) could be considered by the whole class.
Possible content
Using calculated probabilities to challenge intuitive ideas.
Resources
None.
Solution/Notes
In the first situation there is no difference in the probability of choosing a red ball from box A or box B, it is the same in both cases. The second two situations bring to the fore two fairly common misconceptions regarding probability – in both cases each of the two events are equally probable.
Original Material © Cambridge University Press 2009