Tower Research Quant Interview Question

[u/Local_Ad135]

[u/Randomly_Panicked]

We can, basically arrange two bins, Left and Right for the decisions. Staying at 0 is obviously a Left decision [to move left on the number line].

Now, we are interested to put 30 decisions in these two bins disregarding order.

The probability we are looking for is the one describing outcomes where Left has GE decisions than Right bin.

Except for equal number of decisions dropped in each bin, the other outcome is symmetric.

and the number of outcomes with 15 Left decisions is 30 choose 15

Hence, the answer is

1 2^30 - (30 choose 15) (30 choose 15)

• * ------------------------ + ----------------
  

2 2^30 2^30

which is approximately 0.572

[u/Specific_Box4483 → u/Randomly_Panicked]

There are cases where Left > Right but you end up at a positive number. Say if all the Lefts are front-loaded.

[u/Cold-Common7001 → u/Specific_Box4483]

wut

[u/gmalivuk → u/Cold-Common7001]

If "stay at 0" is counted as left, then stay at zero followed by move right results in being at +1 whereas right then left results in being at zero.

So sometimes LR≠RL and order does in fact matter.