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Conditional Probabilityhard
0:00.0

An email filter marks emails as spam (S) or not spam (N). P(mark S∣actually S)=0.95P(\text{mark }S|\text{actually }S) = 0.95P(mark S∣actually S)=0.95, P(mark N∣actually N)=0.90P(\text{mark }N|\text{actually }N) = 0.90P(mark N∣actually N)=0.90. 5% of emails are actually spam. What is P(actually S∣marked S)P(\text{actually }S|\text{marked }S)P(actually S∣marked S)?