The occurrence of a disease is 1/100=P(D) The false negative probability is 6/100=P(−|D), and the false positive is 3/100=P(+|¬D) Compute P(D|+) By bayes formula, P(+)=P(+|D)P(D)+P(+|¬D)P(¬D)=97/10000+297/10000=394/10000 Similarly P(D|+)=(P(+|D)P(D))/(P(+))=97/394=0.246

Kymani Hatfield

Kymani Hatfield

Answered question

2022-11-01

The occurrence of a disease is 1 100 = P ( D )
The false negative probability is 6 100 = P ( | D ), and the false positive is 3 100 = P ( + | ¬ D )
Compute P ( D | + )
By bayes formula,
P ( + ) = P ( + | D ) P ( D ) + P ( + | ¬ D ) P ( ¬ D ) = 97 10000 + 297 10000 = 394 10000
Similarly P ( D | + ) = P ( + | D ) P ( D ) P ( + ) = 97 394 = 0.246
Is this correct?

Answer & Explanation

Marlene Welch

Marlene Welch

Beginner2022-11-02Added 23 answers

No,
P [ D | T + ] = P [ T + D ] P [ T + D ] + P [ T + D ¯ ] = ( 100 6 ) × 1 ( 100 6 ) × 1 + 3 × ( 100 1 ) = 24.04
Notes
- data in % to avoid lot of decimals, so the result is 24.04 %
All the data expressed in formulas, e.g ( 100 1 ), mean that they are calculated and not given by the text

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