Mastering Combinatorics: My Challenging Maven Securities Trader Internship Test

Software Engineering
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mavensecurities | Trader Summer Internship | Interview Experience

Interview Date: Not specified
Result: Not specified
Difficulty: Not specified

Interview Process

Completed an online test as part of the application for the Trader Summer Internship. The test consisted of multiple-choice questions focused on math, probability, and logic.

Technical Questions

  1. Combinatorics: There are 100 teams playing in a knock-out competition. What is the least number of games to be played to decide the winner assuming no games are drawn?
    A) 50, B) 98, C) 99, D) 100, E) 101

  2. Probability: Suppose we have a circular table, on which 3 legs are placed uniformly at random around the circumference of the tabletop. What is the probability the table can stand?
    A) 0, B) 1/4, C) 1/3, D) 1/2, E) 1

  3. Probability: A 6-sided die is rolled and summed repeatedly until the sum is 100 or more. What is the most likely last roll?
    A) 1, B) 3, C) 4, D) 5, E) 6

  4. Probability: There are three cookie boxes: the first contains 20 chocolate cookies, the second contains 10 oat cookies, and the third box contains a mix of chocolate, oat, and raspberry cookies (5 of each). Given we take two cookies from a box at random and both are chocolate, what is the probability we took them from the first box?
    A) 1/2, B) 2/3, C) 41/46, D) 21/23, E) 10/11

  5. Probability: You shuffle a pack of 54 regulation playing cards, including jokers. What is the average number of cards required to be turned over to produce the first ace?
    A) 10, B) 10.5, C) 11, D) 13.5, E) 16

  6. Probability: In a knockout squash tournament with 8 players, assuming the best player always beats the next best, what is the probability the second-best player makes the final?
    A) 3/8, B) 1/2, C) 4/7, D) 7/8, E) 1

  7. Combinatorics: There are 10 6-sided dice labeled from 1-10. How many different combinations can we get to have their face values sum to 16?
    A) 3003, B) 5005, C) 8008, D) 8010, E) 11440

  8. Probability: A certain disease affects 1% of the population. A medical test is developed, but is imperfect. If a person has the disease, they test positive 99% of the time; if they do not have the disease, they test positive 5% of the time. Given someone tests positive, what is the approximate probability they actually have the disease?
    A) 17%, B) 20%, C) 84%, D) 98%, E) 99%

Tips & Insights

Practice solving problems related to combinatorics and probability, as these were heavily featured in the test. Familiarity with statistical concepts and logical reasoning is crucial for success in this type of interview.