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8 problems: (1) 'P(rain)=0.3, P(clouds|rain)=0.9, P(clouds|no rain)=0.4. It's cloudy. P(rain|clouds)?' (2) 'Spam filter: P(spam)=0.2, P(word 'free'|spam)=0.8, P('free'|not spam)=0.1. Email contains 'free'. P(spam|'free')?' (3) 'Factory: Machine A (60% of production, 3% defective), Machine B (40%, 5%

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