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factors probability tasks

100 Rolls Task

**Update November 2020. Jamie Mitchell–a fantastic teacher from Ontario, Canada–sent me this google doc that his student prepared to justify her solution. After you wrestle with the prompt for a while, take a second to read this brilliant response!

Most probability resources contain a familiar type of question: the two-dice probability distribution problem. 

Often times, it is accompanied with questions concerning the sums of the faces that appear on each dice. 

For example:

Roll two fair, 6-sided dice. What possible sums can be made by adding the faces together?
What is the probability that:
a) the sum is 6
b) the sum is a multiple of 4
c) the sum is greater than 15?