The subject line says "urgent," is the ticket really urgent?

Question

A help desk finds that 20\% of tickets are genuinely urgent and 80\% are routine. The word "urgent" appears in the subject line of 75\% of genuinely urgent tickets, but also in 5\% of routine tickets. A new ticket has "urgent" in its subject. What is the probability the ticket is genuinely urgent?

Accepted Answer

Imagine 1{,}000 tickets: 200 urgent and 800 routine. Count the ones saying "urgent." - Urgent with the word: 200 	imes 0.75 = 150. - Routine with the word: 800 	imes 0.05 = 40. Of the 150 + 40 = 190 tickets containing "urgent," 150 are genuinely urgent: P(	ext{urgent} \mid 	ext{word}) = \frac{150}{190} = \frac{15}{19} \approx 0.789. The keyword is much more common in truly urgent tickets, so it raises belief from the 20\% base rate to about 79\%. Takeaway. A clue that is both frequent in the target class and rare outside it produces a strong, reliable update.

The subject line says "urgent," is the ticket really urgent?

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