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Limiting Probabilities

Age 16 to 18
Challenge Level

The question requires an understanding of the definition of matrix multiplication and of the probability formulae $$p(u\ {\rm and}\ v) = p(u)\times p(v)$$ and $$p(u\ {\rm or}\ v) = p(u)+ p(v)$$
You will want to use a calculator (or software) that will work out matrix products for you.