What is the probability that it was categorized by S1?

Three spam email filtering systems S1, S2 and S3 categorise respectively 40%, 10% and 50% of the incoming email messages at a company. The percentage of wrong category decisions if S1 is used is 5%, if S2 is used is 3% and if S3 is used is 6%. An incoming email is selected at random: a) 

Find the probability that the email was wrongly categorised (10 marks) Answer is 

0.053. Formula is: P(WC) = P(S1)(WC|S1)+P(S2)(WC|S2)+P(S3)(WC|S3) = 0.4x0.05 + 0.1x0.03 + 0.5x0.06 = 0.053

(b) If the email was wrongly categorised, find the probability that it was categorised by system S1 (10 marks

I don't know the formula for answering (b)

2 Answers

  • Amy
    Lv 7
    1 month ago

    P(S1|WC) = P(S1 & WC) / P(WC)

  • Anonymous
    1 month ago

    move to homework help.

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