Optiver quant research OA

Has anyone done the OA for this recently? Please help!!!

You’ll get a mix of stats, brain teasers, probability, math etc. A sample of recent questions:

  1. 20 dishes and 40 people, what is the expected number of different dishes picked if each person orders one dish?
  2. Given a 3x3 matrix,solve for a such that the determinant = 0.
    1 cos(E) a
    cos(E) 1 cos(F)
    a cos(F) 1
  3. The correlation between A and B is 0.8, correlation between B and C is 0.7. What’s the correlation between A and C?
  4. a+b=28, b-c=4, a*c=112, solve for a, b and c
  5. Betting probabilities
  6. You’re throwing two dice. You know one shows a 6, what’s the probability the other is also 6?
  7. Now you throw N dice and see one 6, what’s the probability all the others are 6?
  8. Determinant of M-I, where M is a matrix with all elemen‍‍‌‌‌‌‌‍‌‍‌‌‌‍‍‌‌‌‍‌ts being 1, I is the identity matrix

Coding questions:

Hope this helps. Don’t panic, just prepare well for it!

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Thank you again, this was very helpful!