You are trying to design a system that will determine whether someone has a PhD in...

You are trying to design a system that will determine whether someone has a PhD in music. You have the following information:

The probability that a music PhD can correctly identify a composer from a 5-second audio clip is 85%
The probability that anyone else can identify a composer from a 5-second audio clip is 2%
Music PhDs make up 0.3% of the population

You stop someone on the street and play them a 5-second segment of Claire de Lune. They correctly identify the composer as Debussy. Based on the information above, what is the probability that this person has a music PhD?

Expert Solution

P(correctly identify a composer | music PhD) = 0.85

P(correctly identify a composer | anyone else) = 0.02

P(music PhD) = 0.003

P(correctly identify a composer) = P(correctly identify a composer | music PhD) * P(music PhD) + P(correctly identify a composer | anyone else) * P(anyone else)

= 0.85 * 0.003 + 0.02 * (1 - 0.003)

= 0.02249

P(music PhD | correctly identify a composer) = P(correctly identify a composer | music PhD) * P(music PhD) / P(correctly identify a composer)

= 0.85 * 0.003 / 0.02249

= 0.1134

orchestra answered 2 years ago

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