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Old Mission Capital QT OA ：35 MCQ

Quantitative researcher · New GradBachelor's degreeSep 2026

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Sep 26, 2026

This is a summary based on publicly available interview reports for the Old Mission Capital Junior Quant Trader OA.

1. OA Format

Based on reports from 2024 New Grad Junior Quant Trader candidates:

Around 35 multiple-choice questions + 1 coding problem
The multiple-choice section was roughly 25–35 minutes
The coding section was around 30 minutes
Python was recommended for the coding portion
Calculators were allowed
Probability answers were usually expected in simplified fractions or exact decimals

One thing that comes up repeatedly in candidate reports is that speed is the biggest challenge.

Most individual questions are not extremely difficult, but there are a lot of them, so spending too much time on the first 10–15 questions can hurt you later.

The coding section seems relatively manageable time-wise. A simple working solution is usually better than spending too much time trying to fully optimize it.

Some candidates who moved on to later rounds also reported questions involving probability, mental math, and situational/behavioral questions.

2. Publicly Reported Question Types & Answers

Here are some examples that have appeared in public reports:

Two dice sum to 8:
Answer: 5/36
26 people all shake hands with each other once:
Answer: C(26,2) = 325
1/50 products are defective. You earn $3 on a good product and lose $75 on a defective one. What is the expected profit?
Answer: $1.44
Given that two dice sum to 9 and one of the dice is a 5, what is the probability of the possible outcome?
Answer: 1/2
Pick a random card numbered 1–30 and receive 6 times the number on the card:
Expected value: $93
Draw from two containers. Probability of getting the same color:
Answer: 37/72
Choose two numbers without replacement from 1–15. Probability their sum is odd:
Answer: 8/15
Probability that the first two cards drawn from a standard deck are both Jacks:
Answer: 1/221
Flip a fair coin five times. Probability all five flips are the same:
Answer: 1/16
Flip two coins. You win $2 for each head, but lose $7 if both are tails. Expected value:
Answer: $0.25
Probability that HHH appears before TTTT:
Answer: 15/22
There are 3 large donuts and 9 small donuts, with a process continuing until only small donuts remain. Expected time:
Answer: 131/12 ≈ 10.917 hours

Old Mission Capital QT OA Questions

2025 (Jul–Sep)
Role: Quant Finance / New Grad
Reported in April, 2025

Format: 35 questions in 25 minutes

Question 24 is missing here, but it was reportedly very easy.

Question List

1. Dice Sum

What is the probability that the sum of two dice is 8?

2. Handshakes

In a group of 26 people, if everyone shakes hands with everyone else exactly once, how many handshakes occur in total?

3. Expected Profit

A company manufactures widgets, but 1 out of every 50 is defective.

Profit on a working widget: +$3
Loss on a defective widget: -$75

What is the expected profit per widget?

4. Conditional Probability with Dice

I just rolled a total of 9 with two dice.

What is the probability that one of the dice showed a 5?

5. Expected Value of a Card Game

There are 30 distinct cards numbered from 1 to 30.

You draw one card uniformly at random, and I pay you:

6 × the number on the card

What is the expected value of this game?

6. Matching Ball Colors

Jar A

3 red balls
5 black balls

Jar B

4 red balls
5 black balls

If one ball is drawn at random from each jar, what is the probability that the two balls are the same color?

7. Odd Sum

A jar contains 15 balls, numbered from 1 to 15.

Two balls are drawn without replacement.

What is the probability that their numbers sum to an odd number?

8. Pair of Jacks

What is the probability that the first two cards drawn from a standard deck are both Jacks?

9. Five Identical Coin Flips

A fair coin is flipped 5 times.

What is the probability that all five flips show the same side?

10. Fair Value of a Coin Game

A player flips 2 coins.

Win $2 for each head
Lose $7 if both coins are tails

What is the fair value of this game?

11. Double-Headed Coin

A jar contains 12 coins:

10 fair coins
2 double-headed coins

One coin is chosen at random and flipped 5 times.

All five flips are heads.

What is the probability that the selected coin was double-headed?

12. Repeated Half-Bankroll Betting

You start with $64 and make 6 consecutive bets.

On every bet, you wager half of your current bankroll.

If you win 3 times and lose 3 times, how much money do you gain or lose?

13. Safe vs. Unsafe Drivers

An insurance company knows:

Unsafe drivers have a 40% chance of an accident in a year
Safe drivers have a 10% chance
85% of drivers are safe

Given that a driver had an accident, what is the probability that the driver is unsafe?

14. Ordered Ball Draws

A jar contains:

7 red balls
10 black balls

Four balls are drawn without replacement.

What is the probability that:

The first two are red
The next two are black

15. Shoes Without a Complete Pair

A closet contains 5 pairs of shoes.

If 5 individual shoes are selected at random, what is the probability that no complete pair is selected?

16. Pair from a Deck

What is the probability that the first two cards drawn from a standard deck form a pair?

17. HH Before TH

You and your friend repeatedly flip a fair coin.

If HH appears first, you win
If TH appears first, your friend wins

What is the probability that you win?

18. Horse Race

There are 8 horses in a race.

What is the probability that:

Horse #4 finishes second
Horse #1 finishes in the top three

19. Expected Losing Score

A fair coin is flipped repeatedly.

Heads → I get 1 point
Tails → You get 1 point

The game ends when either player reaches 3 points.

What is the expected score of the loser?

20. Three Dice Sum

Three fair dice are rolled.

What is the probability that their sum is 14?

21. Party Invitations

A person has 9 friends and wants to invite 6 of them.

Two of the friends do not get along and will not attend together.

How many valid invitation groups are possible?

22. Circular Bracelet

How many distinct circular bracelets can be made using:

3 red beads
3 green beads

23. Blackjack Probability

What is the probability of being dealt a blackjack?

A blackjack means drawing:

One Ace
One card from 10, J, Q, K

The two cards are drawn without replacement.

24. Skipped

Question 24 was not included in the report.

25. Palindromes of `MISSISSIPPI`

How many palindromic arrangements can be formed using the letters in:

MISSISSIPPI

26. Exactly Two Majors

A university offers only three majors:

Computer Science
Mathematics
Philosophy

The student population is distributed as follows:

50% major in Mathematics
60% major in Computer Science
20% major in Philosophy
6% major in all three

What percentage of students major in exactly two subjects?

27. Fair Value of an Option-Like Right

An energy company is drilling for oil.

Probability of success: 35%
Probability of failure: 65%
Stock value if successful: $100
Stock value if unsuccessful: $16
Current stock price: $58.50

You have the right to buy the stock for $70 on the day after the drilling result becomes known.

What is the fair value of this right?

28. Party on the First Sunny Day

You want to host a party over the weekend.

Probability of rain on Saturday: 70%
Probability of rain on Sunday: 60%

You will hold the party on the first day without rain.

By Monday, you know the party happened and your friends enjoyed it.

What is the probability that the party was held on Saturday?

29. Same Row or Column

Two squares are selected uniformly at random from an 8×8 chessboard.

What is the probability that the two selected squares share the same:

Row, or
Column

30. Another Pair After Two 8s

Two cards are drawn without replacement from a standard 52-card deck.

The first two cards are both 8s.

You then draw two more cards.

What is the probability that the next two cards also form a pair?

31. Last Red Ball by Draw 5

A bag contains:

3 red balls
5 black balls

Balls are drawn one at a time, uniformly at random, without replacement.

What is the probability that the last red ball is drawn on or before the 5th draw?

32. First Ace Appears at Position 33

A standard shuffled deck is revealed one card at a time.

The first Ace appears as the 33rd card.

What is the probability that the 34th card is the 7 of Diamonds?

The answer is not 1/51.

33. Candy Conveyor Belt

On a candy conveyor belt:

4 out of every 5 chocolates are followed by a jelly bean
2 out of every 3 jelly beans are followed by a chocolate

What fraction of all candies on the conveyor belt are jelly beans?

34. HHH Before TTTT