Top 25 Quant Interview Questions for Freshers (With Clear Explanations)
Are you preparing for your first quant interview? Whether you’re aiming for a job in quantitative finance, data science, or analytics, you’re likely to face a mix of probability, statistics, mental math, logic, and basic finance questions. In this guide, we’ve compiled 25 of the most common quant interview questions for freshers, each with clear, step-by-step explanations. Let’s help you build confidence and ace your upcoming interview!
Top 25 Quant Interview Questions for Freshers (With Clear Explanations)
1. What is the probability of getting at least one six in four throws of a fair die?
Let’s calculate the probability step by step:
- Step 1: The probability of NOT getting a six in one throw = \( \frac{5}{6} \)
- Step 2: Probability of NOT getting a six in four throws = \( \left( \frac{5}{6} \right)^4 \)
- Step 3: Probability of getting AT LEAST one six = 1 - Probability of getting NO sixes
So,
\[ P(\text{at least one six}) = 1 - \left( \frac{5}{6} \right)^4 = 1 - \frac{625}{1296} \approx 0.5177 \]
Intuition: It’s easier to calculate the probability of the opposite event (no sixes) and subtract from 1.
2. Explain the difference between variance and standard deviation.
Both measure the spread of data, but there’s a key difference:
- Variance (\( \sigma^2 \)): The average of the squared differences from the mean.
- Standard Deviation (\( \sigma \)): The square root of the variance.
\[ \text{Variance:} \ \sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2 \] \[ \text{Standard Deviation:} \ \sigma = \sqrt{\sigma^2} \]
Intuition: Standard deviation is in the same units as the data, making it easier to interpret.
3. A coin is tossed 3 times. What is the probability of getting exactly two heads?
This is a binomial probability problem.
- Total possible outcomes: \( 2^3 = 8 \)
- Ways to choose 2 heads out of 3: \( \binom{3}{2} = 3 \)
- Probability for each favorable outcome: \( \left(\frac{1}{2}\right)^3 = \frac{1}{8} \)
So,
\[ P(\text{exactly 2 heads}) = 3 \times \frac{1}{8} = \frac{3}{8} \]
Intuition: Use combinations to count favorable outcomes.
4. What is the expected value of a fair six-sided die roll?
The expected value is the average outcome if you roll the die many times.
\[ E[X] = \sum_{i=1}^6 i \cdot P(i) = \sum_{i=1}^6 i \cdot \frac{1}{6} \] \[ = \frac{1 + 2 + 3 + 4 + 5 + 6}{6} = \frac{21}{6} = 3.5 \]
Intuition: Expected value is a “long-run” average.
5. If two events are independent, what can you say about their joint probability?
For independent events A and B:
\[ P(A \cap B) = P(A) \times P(B) \]
Intuition: Independence means one event doesn’t affect the probability of the other.
6. What is the probability of drawing 2 aces in a row from a standard deck (without replacement)?
There are 4 aces and 52 cards in total.
- Probability first card is an ace: \( \frac{4}{52} \)
- Probability second card is an ace: \( \frac{3}{51} \) (since one ace is already drawn)
- Multiply the probabilities:
\[ P = \frac{4}{52} \times \frac{3}{51} = \frac{1}{221} \]
Intuition: Count the favorable outcomes step by step, updating the total cards each time.
7. There are 6 doors, behind one is a car, behind the rest are goats. You pick a door, then the host opens 4 other doors showing goats. Should you switch to the last unopened door?
This is a version of the Monty Hall problem.
- Initial probability car is behind your door: \( \frac{1}{6} \)
- Probability car is behind another door: \( \frac{5}{6} \)
- The host reveals 4 goats, leaving just one other door unopened.
Conclusion: Yes, you should switch! Your chance of winning goes up to \( \frac{5}{6} \) if you switch.
Intuition: The host’s action gives you extra information, making the switch the better choice.
8. What is a normal distribution?
A normal distribution is a bell-shaped, symmetric probability distribution described by its mean (\( \mu \)) and standard deviation (\( \sigma \)). The formula is:
\[ f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{(x - \mu)^2}{2 \sigma^2}} \]
Intuition: Many real-world phenomena (like heights, test scores) are normally distributed.
9. What is the median of the following set: 8, 3, 10, 6, 2?
First, sort the set: 2, 3, 6, 8, 10. The median is the middle value.
Answer: 6 is the median.
Intuition: Median divides the data into two equal halves.
10. What is conditional probability? Give an example.
Conditional probability is the probability of event A given that event B has occurred:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
Example: If there are 3 red and 2 blue balls in a bag, and you pick one ball, what is the probability it is red given it’s not blue? Since “not blue” means “red”, the probability is 1.
Intuition: Conditional probability updates the chance based on new information.
11. How would you mentally calculate 16 × 25?
Break it up:
- 16 × 25 = (16 × 100) / 4 = 1600 / 4 = 400
Intuition: Recognize 25 as a quarter of 100 to simplify multiplication.
12. What is Bayes’ Theorem?
Bayes’ Theorem updates the probability of a hypothesis given new evidence.
\[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \]
Example: If a test for a disease is 99% accurate, but the disease is rare, Bayes’ theorem helps find the real chance you have the disease if you test positive.
Intuition: It combines new evidence with prior belief.
13. In a sequence of coin tosses, how many tosses on average until you see two heads in a row?
Let’s define:
- E = expected tosses until 2 heads in a row
This is a classic Markov process. The answer is 6 tosses.
Intuition: There’s a chance you get a tail and have to start over; so, on average, it takes longer than just 2 tosses.
14. Explain the difference between permutation and combination.
- Permutation: Order matters. Number of ways to arrange n objects = \( n! \).
- Combination: Order does not matter. Number of ways to choose r objects from n = \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \).
Intuition: Use permutations for order, combinations for groups.
15. In a standard deck, what is the probability of drawing a heart or a king?
- Number of hearts: 13
- Number of kings: 4
- But one king is also a heart, so count it only once.
- Total = 13 + 3 = 16
\[ P = \frac{16}{52} = \frac{4}{13} \]
Intuition: Subtract overlap to avoid double-counting.
16. What is the sum of the first 100 natural numbers?
Use the formula:
\[ S = \frac{n(n + 1)}{2} \] Where \( n = 100 \): \[ S = \frac{100 \times 101}{2} = 5050 \]
Intuition: Pair numbers from each end (1+100, 2+99, etc.).
17. If the price of a stock increases from \$50 to \$55, what is the percentage return?
\[ \text{Return (\%)} = \frac{(\$55 - \$50)}{\$50} \times 100\% = \frac{5}{50} \times 100\% = 10\% \]
Intuition: Percentage change is (change/original) × 100%.
18. What is a p-value?
A p-value is the probability of getting a result at least as extreme as the observed one, under the null hypothesis.
Intuition: Small p-value means the observed result is unlikely by chance; might reject the null hypothesis.
19. If 3 dice are rolled, what is the probability that all show different numbers?
- Total outcomes: \( 6 \times 6 \times 6 = 216 \)
- First die: 6 options
- Second die: 5 options (different from first)
- Third die: 4 options (different from first two)
- So, favorable outcomes: \( 6 \times 5 \times 4 = 120 \)
\[ P = \frac{120}{216} = \frac{5}{9} \]
Intuition: Multiply choices for each step, then divide by total.
20. What is the formula for compound interest, and how does it differ from simple interest?
- Simple Interest: \( SI = P \times r \times t \)
- Compound Interest: \( A = P(1 + \frac{r}{n})^{nt} \), where n is number of times interest is compounded per year.
Intuition: Compound interest earns “interest on interest” and grows faster.
21. How do you find the probability of at least one event happening?
Use the complement rule:
\[ P(\text{at least one}) = 1 - P(\text{none}) \]
Intuition: Sometimes it’s easier to calculate none, then subtract from 1.
22. What is the 80/20 rule (Pareto Principle) in finance?
The 80/20 rule states that roughly 80% of results come from 20% of causes. In finance, 80% of profits might come from 20% of investments.
Intuition: Focus attention where it matters most.
23. Given the mean is 20 and variance is 25, what is the standard deviation?
\[ \text{Standard Deviation} = \sqrt{25} = 5 \]
Intuition: Standard deviation is the square root of variance.
24. What is arbitrage?
Arbitrage is the practice of taking advantage of price differences in different markets to make a risk-free profit.
Example: Buy an asset at a lower price in one market and sell at a higher price in another.
Intuition: Arbitrage opportunities do not last long in efficient markets.
25. If a stock has a beta of 1.5, what does that mean?
Beta measures a stock's volatility compared to the market:
- Beta = 1: Moves with the market
- Beta &
- Beta < 1: Less volatile than the market
- Beta > 1: More volatile than the market
So, if a stock has a beta of 1.5, it is 50% more volatile than the overall market. If the market goes up by 1%, the stock is expected to go up by 1.5% (and vice versa).
Intuition: Beta helps investors understand risk relative to the broader market.
Bonus: Quick Quant Interview Tips for Freshers
- Understand the Concepts: Don’t just memorize formulas—know when and why to use them.
- Practice Mental Math: Quick calculations impress interviewers and save time on logic/finance questions.
- Explain Your Reasoning: Interviewers are interested in your thought process as much as the answer.
- Brush Up on Probability and Statistics: These are the backbone of most quant interviews.
- Stay Calm: If you get stuck, talk through your thinking. Partial credit is often given for good logic.
Summary Table: Top 25 Quant Interview Questions and Explanations
# Question Key Concept Short Answer 1 Probability of at least one six in four throws of a fair die? Probability, Complement Rule \(1 - (\frac{5}{6})^4 \approx 0.5177\) 2 Difference between variance and standard deviation? Statistics, Measures of Spread Variance = squared spread, Std Dev = square root of variance 3 Probability of exactly two heads in three coin tosses? Combinatorics, Binomial \(\frac{3}{8}\) 4 Expected value of a fair die roll? Expected Value 3.5 5 Joint probability for independent events? Independence, Probability Multiply probabilities: \(P(A) \times P(B)\) 6 Probability of 2 aces in a row (no replacement)? Conditional Probability \(\frac{1}{221}\) 7 Monty Hall problem with 6 doors—switch? Probability, Game Theory Yes, switch; win chance is \( \frac{5}{6} \) 8 What is a normal distribution? Statistics, Distributions Bell-shaped, symmetric, defined by \(\mu\) and \(\sigma\) 9 Median of 8, 3, 10, 6, 2? Statistics, Median 6 10 What is conditional probability? Probability \(P(A|B) = \frac{P(A \cap B)}{P(B)}\) 11 Mentally calculate 16 × 25 Mental Math 400 12 What is Bayes’ Theorem? Bayesian Probability \(P(A|B) = \frac{P(B|A)P(A)}{P(B)}\) 13 Avg. tosses for two heads in a row? Markov Process 6 tosses 14 Permutation vs Combination? Combinatorics Permutation: order matters; Combination: order doesn't 15 Probability of drawing a heart or king? Set Theory, Probability \(\frac{4}{13}\) 16 Sum of 1 to 100? Sequences, Arithmetic 5050 17 Stock \$50 to \$55: % return? Finance, Return Calculation 10% 18 What is a p-value? Statistics, Hypothesis Testing Probability of observed/extreme result under null 19 Probability 3 dice all different? Counting, Probability \(\frac{5}{9}\) 20 Compound vs Simple Interest? Finance, Interest Compound: earns on interest, grows faster 21 Probability at least one event? Complement Rule \(1 - P(\text{none})\) 22 What is the 80/20 rule? Pareto Principle, Finance 80% results from 20% causes 23 Mean 20, variance 25: standard deviation? Statistics 5 24 What is arbitrage? Finance, Markets Risk-free profit from price differences 25 Stock beta 1.5: meaning? Finance, Risk 50% more volatile than the market
Frequently Asked Questions (FAQs) about Quant Interviews
- How should I prepare for a quant interview as a fresher?
Focus on probability, statistics, basic finance, logic, and mental math. Practice with mock questions and explain your reasoning.
- What are interviewers looking for in quant interviews?
They want to see your problem-solving process, logical thinking, and how you handle pressure. Communicating your thought process is key!
- Should I memorize formulas?
Know key formulas, but more importantly, understand when and how to use them.
- What topics are most important?
Probability, statistics, combinatorics, mental math, basic finance, and some logic puzzles are the most common.
- How do I improve my speed?
Practice regularly with mental math and timed quizzes. Break down complex problems into simpler steps.
Conclusion
Quant interviews can be challenging, but with the right preparation and mindset, you can excel even as a fresher. Focus on understanding the intuition behind each question—not just the answer. Practice explaining your reasoning, stay calm under pressure, and you’ll stand out from the competition.
Good luck with your quant interview!
