Tuesday, November 29, 2011

Quiz Time: Bayesian Judgement

My friend rates himself as a pretty good connoisseur of wine. To his credit, when I gave him a taste-test some time ago, he could correctly identify a wine variety around 80% of the time.

Last week I bought a mixed case containing 10 bottles of Merlot and 2 of Shiraz. I then took a bottle at random and poured my friend a glass. He said he thought it was a Shiraz.

What is the probability that the bottle actually was a Shiraz?

2 comments:

  1. The answer will appear here in a few days.

    Meanwhile it might help to consider the probability of a false-positive i.e. the likelihood that the bottle is a Merlot but my friend thought it was a Shiraz.

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  2. Answer:

    At the start, there are four possible outcomes:

    1. A merlot, correctly identified, which has a probability of 10/12 * 0.8 = 67%

    2. A merlot, incorrectly identified, prob. = 10/12 * 0.2 = 17%

    3. A shiraz, correctly identified, prob. = 2/12 * 0.8 = 13%

    4. A shiraz, incorrectly identified, prob. = 2/12 * 0.2 = 3%

    If we know that my friend said it was a shiraz, we are in either scenario 2 or scenario 3. i.e. it is more likely that we have a false positive than an actual shiraz.

    The probability that it is actually a shiraz is 13/(13+17) = 44%

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