# Practice Questions for the Quantitative Finance Interview

## Statistics and mathematics sample questions for interview practice.

Quantitative finance interviews are notorious for grilling candidates on programming, statistics, mathematics, finance, and brain-teaser style questions. While these interviews can often be quite tricky, there are plethora of practice resources you can leverage to quickly familiarize yourself with these kinds of questions and eventually be able to ace the interviews.

In this article, I’ll cover a handful of practice problems, in the domain of statistics and mathematics, that may serve as a sample of what you may be asked during a quant interview. These questions were collected from online assessments that were conducted by candidates pursuing jobs in quantitative research and quantitative trading. If you're interested in finding more quant interview questions you can find some here. Without further ado, let’s get into it.

## Question 1

A certain disease has an incidence rate of 2%. If the false negative rate is 10% and the false positive rate is 1% compute the probability that a person who tests positive actually has the disease?

*Answer Below*

The answer to this question can be derived from having knowledge about Bayes theorem. Bayes theorem helps describe the probability of an event **A** occurring based on the prior knowledge we know **B**. Mathematically, this is expressed as

In this scenario, lets say that **A** refers to the event that the person actually has the disease, and **B** refers to the event that the person has tested positive. Our equation now becomes:

Given that the problem statement says that the incidence rate is 2%, we can say that

To find the remaining pieces in the equation, we can construct the following matrix.

Positive | Negative | |
---|---|---|

Has Disease | True Positive Rate | False Negative Rate |

Does Not Have Disease | False Positive Rate | True Negative Rate |

By substituting in the values that we are provided in the problem statement, we get

Positive | Negative | |
---|---|---|

Has Disease | 1 - 0.1 | 0.1 |

Does Not Have Disease | 0.01 | 1 - 0.01 |

Using the matrix above, we see that the probability that a person tests positive, given that they have the disease, is 90%. In order to calculate the probability that someone tests positive we can use the law of total probability. This equates to:

Using these values, we can arrive at the following answer.

Therefore, the probability that a person who tests positive actually has the disease is 64.7%

## Question 2

2020 people stand in a circle and are numbered from 1 to 2020. Person 1 is skipped and Person 2 is sent out of the circle. Person 3 is skipped and Person 4 is sent out of the circle. If this process repeats until only one person is left in the circle, what number Person will that be? Answer choices: a) 996 b) 1993 c) 897 d) 1024

*Answer Below*

This is a common problem in mathematics that has been termed the Josephus problem. The first step in solving this problem is to calculate the difference between the total number of people and the nearest number that is a power of 2 which is smaller than the total number of people. In this case the total number of people is 2020 and we know that 2 to the power of 11 is 2048 (too big) and 2 to the power of 10 is 1024. We can now calculate 2020 - 1024 = 996. Finally, to find the number of the last person standing we do 2 * 996 + 1 = 1993. Therefore the answer is b.

## Question 3

You are shooting arrows at a target with three rings: there is a circle with a 4 inch radius, a ring around it with 8 inch radius, and a ring around that with a 12 inch radius. If your 3 arrows will hit the target somewhere uniformly at random, what is the probability that you land exactly one shot in each of the three rings? Answer choices: a) 5/243 b) 10/243 c) 5/81 d) 10/81

*Answer Below*

In order to solve this question, we can calculate the individual probabilities of landing an arrow in each of the circles. We can calculate this probability as the area of the circle divided by the total area of the target.

The total area of the target can be calculated as:

Next, the area of the smallest circle can be calculated as:

We can define the probability of an arrow landing in this circle as the circle's area divided by the total area of the target. Mathematically, this can be expressed as:

Next, we calculate the area of the first ring and the probability of hitting it. Note that in order to calculate the area of the first ring we must subtract away the area of the inner circle.

Finally, we calculate the probability of the arrow landing in the second ring as 1 minus the probabilities of the arrow landing in one of the other two rings.

With these three probabilities, we can calculate the probability that we land one arrow in each region as the product of the individual probabilities for each region times the permutations (i.e the number of different ways we can throw the three arrows).

The final result is shown below:

Therefore the correct answer choice is d.

## Bonus Questions

If you enjoyed the previous questions, here are two more that you can try on your own.

### Bonus 1

Let there be a 20% chance of rain on any day. If the meteorologist forecasts rain, there is a 30% chance of rain. He uses yesterday's weather to consider forecasting rain. If there was rain, he uses a fair coin toss to decide whether to forecast rain again. What is the probability the meteorologist makes a correct forecast for rain? Answer choices: a) 6% b) 15% c) 10% d) 3%

### Bonus 2

Find the number of 8-digit numbers ABCDEFGH with distinct digits from 1 to 8 such that A > B > C > D and D < E < F < G < H. Answer choices: a) 24 b) 48 c) 70 d) 35

## Closing Remarks

Thanks for reading this article. We hope that the questions covered here have helped you with your preparation for any upcoming quantitative finance interviews. If you're currently in the process of looking for a job or internship in quantitative finance check out OpenQuant for the best quant jobs.