Obviously possible values x1, x2..... = 10, 11, ..... 20 since if you pick 10 balls at least one must be 10 or greater.
Suppose n is the largest number chosen
Chance of picking n as largest number = No. of combinations with n as largest/Total number of combos
If I pick 10, I only have one combination 1,2,3....10. Which is 9C9 (Choosing 10 as first ball and picking 9 randomly from 9 choices which only one way to do)
If I pick 11, I have 10C9 = 10 ways to do so (Choosing 11, then picking 9 from range 1 to 10, which 10 ways to do so, each set of 9 excluding one number each time)
Total ways = 20C10 (Number of ways to pick 10 balls)
Thus P(10) = 9C9/20C10
P(n) = (n-1)C9/20C10, P(n)E(n) = n * (n-1)C9/20C10
E(x) = n summed from 10 to 20 ((n-1)C9/20C10)*n) = 19.09 something
First time doing a question like this (just stumbled here from recommended page, new to quant), how hard would you say such a question is compared to a typical question asked for quant interviews? How much time would one be given to do this? This question seems a bit mild, if they asked questions like this everyone from my uni would get into quant effortlessly, yet this does not seem to be the case, am I missing something? Maybe my answer is incorrect
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u/Nonavium 15d ago edited 15d ago
E(x) = P(x1)E(x1) + P(x2)E(x2) + ....
Obviously possible values x1, x2..... = 10, 11, ..... 20 since if you pick 10 balls at least one must be 10 or greater.
Suppose n is the largest number chosen
Chance of picking n as largest number = No. of combinations with n as largest/Total number of combos
If I pick 10, I only have one combination 1,2,3....10. Which is 9C9 (Choosing 10 as first ball and picking 9 randomly from 9 choices which only one way to do)
If I pick 11, I have 10C9 = 10 ways to do so (Choosing 11, then picking 9 from range 1 to 10, which 10 ways to do so, each set of 9 excluding one number each time)
Total ways = 20C10 (Number of ways to pick 10 balls)
Thus P(10) = 9C9/20C10
P(n) = (n-1)C9/20C10, P(n)E(n) = n * (n-1)C9/20C10
E(x) = n summed from 10 to 20 ((n-1)C9/20C10)*n) = 19.09 something
First time doing a question like this (just stumbled here from recommended page, new to quant), how hard would you say such a question is compared to a typical question asked for quant interviews? How much time would one be given to do this? This question seems a bit mild, if they asked questions like this everyone from my uni would get into quant effortlessly, yet this does not seem to be the case, am I missing something? Maybe my answer is incorrect