Emilio found an old violin in his grand-grandmother’s attic. He wonders if it is one of those instruments hand-made by the 17th century Italian family Stradivari, which are extremely valuable today. He knows this is highly improbable, but since he is in Italy, it is relatively higher, say 3%. In any case, he starts examining the violin, and sees a label inside: “Antonius Stradivarius 1732”, the “732” part is hand written. He knows that this is a characteristic of Stradivari violins, you’ve read that about 1000 Strads were produced and about 663 of them had such labels. But it is also a marketing strategy used for modern fabricated violins, such that about 39% of non-Strad violins have such labels. What is the probability that the violin is a Strad after this information about the label?

Even more excited, he tries to play the violin. Famous for their extraordinary sound quality, he expects to sound like a professional. However, Emilio is a beginner and what he plays sound quite bad. But how come? There is a very low chance for a beginner to sound good on normal violins (2%), or even on a Strad (5%). What is the probability that the violin is a Strad after all this information (about both label and sound)?