1. Using letters
[ A1.1 Extension Plenary]
Here are some formulae about various probabilities when throwing fair 1 – 6 dice.
When n dice are thrown:
the probability that they all show k or less is
the probability that the highest number showing is k is
the probability of getting at least one six is
Use one or more formulae and your scientific calculator to answer these questions.
Jade throws 10 normal dice. a) What is the probability of 5 being the highest number? b) What is the probability that the dice show 5 or less?
a) How many dice do you need to throw to get at least one 6 with a probability 0.5?
b) How many to get at least one six with a probability of 0.99?
Preamble
These problems re-cap some of the previously encountered work on algebra. Some children might need support in considering using informal trial and improvement in the second question – but if at all possible allow children to “discover” this for themselves.
Possible content
Using unfamiliar equations involving indices, informal trial and improvement.
Resources
Scientific calculator (or a calculator able to calculate powers of numbers). Possibly spreadsheet for (2).
Solution/Notes
1) a) b)
2) Pupils will need to use an informal trial and improvement approach. It is reasonable therefore to allow a range of “correct” answers. It may or may not be profitable to consider issues of rounding and significant figures. a) Between 3 (0.42…) and 4 (0.52 …) throws b) Between 24 and 29 throws (0.987… to …).
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010