A practice trainer for two-stage randomness: a die chooses a number, and that number sets up a second random step — another die, or a run of coin flips. Each round asks for one probability or expectation of the second stage. The move is always the same: freeze the first die at each value, answer the easy one-stage question, then average the answers with equal weights. Type a fraction (any equivalent form counts); the feedback builds the full weighted table.

Two-stage randomness. Freeze the first stage, answer the easy question, then average the answers.