Last Man's Rolls 1

What this probability question tests

This is an easy difficulty probability question that probes your intuition about steady-state and boundary effects in sequential processes. Rather than asking you to compute an exact probability, it asks which outcome becomes most likely when you condition on a specific stopping rule.

The key insight is recognizing that the final roll is constrained by the stopping condition—you stop as soon as your sum reaches or exceeds 100. This means not all rolls are equally likely to be the last one. You will need to think about which values can feasibly bring you over the threshold from different positions, and how the geometry of the problem biases the distribution of final outcomes.

• Conditional probability and stopping rules
• Boundary behaviour in iterative sums
• Counting feasible terminal states