Use simulation to decide whether data are consistent with a proposed model.
Map a random device exactly to a probability model
Problem
Use \(\text{one}~\text{random}~\text{digit}\) from \(0~\text{through}~9\) to model an event with probability \(0.30\). Give the exact success and failure mappings, define \(\text{one}~\text{trial}\), and verify the probability.
Big Picture
What this problem is really about
Start by counting the random device's equally likely outcomes and express the target probability as a fraction of that count. Assign exactly that many outcomes to success, map every remaining outcome to failure, and leave no overlap or gaps. Define one trial to match one use of the device, then verify the induced probabilities sum to one.
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