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GATE Overflow Test Series | Probability | Test 1 | Question: 25

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A spam filter is designed by looking at commonly occurring phrases in spam. Suppose that $70\%$ of email is spam. In $10\%$ of the spam emails, the phrase "online bet" is used, whereas this phrase is only used in $0.5\%$ of non-spam emails. A new email has just arrived, which does mention “online bet”. The probability that it is spam is $\_\_\_\_$
(Answer upto 2 decimal places)
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Let $A$ be the event that email is spam. and $B$ be the event that email contain the phrase "online bet".

The probability that received email is spam when it contain phrase "online bet"

$\qquad = \frac{0.7 \times 0.1}{0.7 \times 0.1 + 0.3 \times 0.005 } = \frac{700}{715} = 0.979.$
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