THE DIAMOND MERCHANT
(partial solution)
Restated 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 D_{1}= "a diamond is found on the 1st examination" 
Let D_{2}= "a diamond is found on the 2nd examination" 
Let D_{3}= "a diamond is found on the 3rd examination" 
Let Z_{1}= "a zircon is found on the 1st examination" 
Let Z_{2}= "a zircon is found on the 2nd examination" 
Let Z_{3}= "a zircon is found on the 3rd examination" 


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 D_{1} D_{2} D_{3}, 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