Re-stated problem A diamond merchant accidentally dropped 3 valuable diamonds and 7 less valuable but similar zircons together into a bowl. To separate the two kinds of gems, the merchant must examine each with a hand lens. What is the probability that the merchant will find the 3 diamonds after 3 examinations? (obviously, two could never be sufficient)

Define a few useful events as follows: Let D1= "a diamond is found on the 1st examination" Let D2= "a diamond is found on the 2nd examination" Let D3= "a diamond is found on the 3rd examination" Let Z1= "a zircon is found on the 1st examination" Let Z2= "a zircon is found on the 2nd examination" Let Z3= "a zircon is found on the 3rd examination"

1st exam above   2nd exam above   3rd exam above

From this point, the student must assign conditional probabilities to each branch of the above tree, or at least to those branches leading to the event in the question at the top of this page.

Thus, we seek the probability of the event D₁ D₂ D₃, in red above. It is important that you now try hard to finish solving this problem on your own, but if you have tried hard, and now wish to see a solution, here is another