quanttest's Introduction

Quantitative Research test

October 13, 2016

In Fall 2016, I applied to a quant trading firm (Jane Street). They had me take a HackerRank test for which I was told it was going to be on 'basic math and probability'. To me, these questions require practice so I thought I would post these questions here as sample questions so that future interviewees can practice and be more prepared than I was.

Time: 30 minutes

4 questions

We randomly select 4 numbers from the set of the first 16 prime numbers, without replacement. What is the probability their sum is even? Why?
You have been chosen to play a game involving a 8-sided die. You get to roll the die once, see the result, and then may choose to either stop or roll again. Your payoff is the sum of your rolls, unless this sum is greater than 8, in which case you "bust" and get nothing. What is your strategy for this game? That is, for each possible outcome of the first roll will you choose stop or to roll again?
A bag has three coins in it which are visually indistinguishable, but when flipped, one coin has a 20% chance of coming up heads, another as a 20% chance of coming up heads, and the last has 60% chance of coming up heads. I randomly draw a coin from the bag and flip it, and the result comes up heads. What is the probability that if I reflip this coin, it will come up heads again? Why?
We have two urns. You can't tell them apart from the outside, but one has four $1 chips and six $10 chips, and the other has three $1 chips and seven $10 chips. You randomly draw a chip from one of the urns and it happens to be a $1 chip. Without replacing this draw, I offer you a chance to draw and keep a chip from either urn. Should you draw from the same urn or the opposite urn, and what is the expected value of the chip you draw? Why?

Good luck. Feel free to compare your solutions against mine afterwards.

Recommend Projects