GATE 2022 ES – Question 53
Emails arrive60% corporate,30% Gmail,5% Yahoo,5% Zoho. Spam fractions are1%,2%,3%,3% respectively, with the same spam filter. Find probability a randomly selected email is spam, in percent to one decimal.
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Correct answer: 1.5 to 1.5
Explanation
Total probability weights each conditional spam rate by account share: $.60(.01)+.30(.02)+.05(.03)+.05(.03)=.015$. Hence **1.5%**. Averaging the four spam percentages equally would ignore their very different traffic shares.