Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2025 / Paper 1 / 10

The two throws are independent, giving $36$ equally likely ordered outcomes in the sample space. A total strictly below $4$ occurs only for $(1,1)$, $(1,2)$ and $(2,1)$. Hence the probability is

The favourable outcomes are $(j,j+1)$ and $(j+1,j)$ for $j=1,\dots ,5$. These are ten distinct ordered outcomes among the $36$ equally likely elements of the sample space, so the probability is