Today we are introducing a new series solving Data Science interview questions at these same companies. We will solve three simple problems asked at Facebook for a Data Science role.

*We have so far solved a few algorithmic/coding problems asked in programming interviews across some of the best companies in the world. Today we are introducing a new series solving Data Science interview questions at these same companies. Many of these places do not have a specialized role for Data Scientists (although that’s changing rapidly). For the rest, a Data Scientist typically solves a logical/mathematical puzzle on a whiteboard. Few of these interviews also ask deep/technical questions on SQL. The rest of the interviews are almost identical to the algorithmic/coding interviews that we have seen so far in this blog. Today, we will solve three simple problems asked at Facebook for a Data Science role. Read along…*

Three ants are sitting at the corners of an equilateral triangle. Each ant randomly picks a direction and starts moving along the edge of the triangle. What is the probability that none of the ants collide? Now, what if it is k ants on all k corners of an equilateral polygon?

Let’s start simple, shall we? Here are two ways of solving this problem, both should be obvious after a little thought:

- How many ways can an ant (at any vertex) move? Precisely two!. All the movements of all three ants are independent are each other. As a result, the total number of movements for all three ants is equal to 2³= 8. How many of these movements result in no-collision? Again, precisely two! (1) All ants moving clockwise, and (2) all ants moving counter-clockwise. As a result, the probability of no collision is simply 2/8 = 0.25. How about k ants? There are again two ways a single ant can move, and hence, k ants can move in 2ᵏ different ways. Just like in the case of a triangle, there are precisely two movements resulting in non-collisions. Again, (1) All ants moving clockwise, and (2) all ants moving counter-clockwise. As a result, the probability of non-collision is simply 1/(2ᵏ-¹).
- The above method was
*frequency counting*, where you count the number of ways the event of interest occurs, and divide it by the total number of ways. Let’s directly calculate the probability of non-collision by calculating the probabilities of two*independent and mutually exclusive events.*

facebook software-development data-science probability interview-que

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The agenda of the talk included an introduction to 3D data, its applications and case studies, 3D data alignment and more.

Topics to study and 20 problems to look over