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 0.994 …). Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010