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Workplace accidents are categorized into three groups: minor, moderate, severe. The probability that a given accident is minor is 0.5, that it is moderate is 0.4, and that it is severe is 0.1. Two accidents occur independently in one month. Calculate the probability that neither accident is severe and at most one is moderate.
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The probability breaks down into three mutually exclusive cases: (A1 minor, A2 minor), (A1 minor, A2 moderate), and (A1 moderate, A2 moderate), where A1 is the first accident, A2 the second. The probabilities for each these cases can be computed, using the independence assumption, by multiplying out the individual probabilities. Adding them up gives the result.

Answer: 0.65
by Bronze Status (6,969 points)

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