(Solution) - Suppose that the probability that a cell is cancerous is -(2025 Original AI-Free Solution)

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Suppose that the probability that a cell is cancerous is AN2/20.
Consider the following data for cell age A and the number of toxic molecules N inside.

Suppose that the probability that a cell is cancerous depends on both the age and the number of toxic molecules. Use the law of total probability to find the overall probability that a cell is cancerous, and show how it is really a version of the sum rule for expectations.