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Breakdown of the interview:
0:00 You work at a shoe factory, and you’re working on creating boxes with pairs of shoes. Currently in front of you, imagine there are 3 pairs of shoes (for a total of 6 individual shoes) with the following sizes: 2 size 4s, 2 size 5s, 2 size 6s. The factory defines an “acceptable” pair as 2 shoes that differ in size by a maximum of 1 size — so a shoe with size 5 and a shoe with size 6 would count as an “acceptable” pair. If you close your eyes, and randomly pick 3 pairs of shoes, without replacement, what is the probability that you end up drawing 3 acceptable pairs?
0:43 The candidate asks clarifying questions
1:17 The candidate breaks down the question and starts brainstorming solutions
2:06 Our instructor analyzes the candidate's initial response to the question and points out what he did well
2:54 The candidate walks through the methodology for his solution, and solves the question correctly.
7:43 Our instructor explains the theory behind this question, and whiteboards a solution for this question. He also shows a snippet of the written detailed solution from the Quant Blueprint course, along with a Python code simulation which shows that the final answer approaches 1/3 with infinite trials. Here's a written solution from the course: https://drive.google.com/file/d/1uJNv...
10:10 The interviewer asks the second question. Say you're flipping a fair coin until you obtain the first H. If the first H occurs on the k'th flip, you're given k balls. We're going to randomly put these k balls into 3 bins, labeled 1 2 and 3. Find the probability that none of these 3 bins end up empty.
10:34 The candidate dissects the question and asks clarifying questions.
11:03 The candidate works through some examples and logically breaks the question down to answer the question effectively.
17:55 The candidate has answered the question correctly, and now summarizes his approach.
20:37 Our instructor breaks down the approach the candidate used and whiteboards the fundamental probability theory behind this question.

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