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?
