old | | Interview Experience
Interview Date: Not specified
Result: Not specified
Difficulty: Not specified
Interview Process
The interview consisted of 35 questions, all identical and presented in the same order. The duration of the interview was 25 minutes.
Technical Questions
- Probability: What is the probability that the sum of two dice is 8?
- Combinatorics: In a group of 26 people, how many total handshakes occur if everyone shakes hands with everyone else?
- Probability: A company produces small parts, with 1 in 50 being defective. If each good part earns $3 and each defective part costs $75 in repair, what is the expected profit per part?
- Probability: I just rolled a 9 with two dice. What is the probability that one of the dice showed a 5?
- Probability: I have 30 unique cards numbered from 1 to 30. If you randomly draw one card, I will pay you the number on the card multiplied by $6. What is the expected value of playing this game?
- Probability: Jar A contains 3 red balls and 5 black balls, and Jar B contains 4 red balls and 5 black balls. What is the probability that the two balls drawn from each jar are of the same color?
- Probability: I have a jar with 15 balls numbered from 1 to 15. If I draw two balls without replacement, what is the probability that the sum of the numbers on the two balls is odd?
- Probability: What is the probability of drawing a pair of Jacks from a deck of cards when drawing the first two cards?
- Probability: What is the probability of getting the same side when flipping a coin five times?
- Probability: A player throws two coins in the air. If either shows heads, they win $2; if both show tails, they lose $7. What is the fair value of this game?
- Probability: A jar contains 12 coins, 10 of which are fair (50% heads, 50% tails), and 2 are biased “double heads” coins. If I randomly select one coin and flip it 5 times, resulting in heads each time, what is the probability that I selected a “double heads” coin?
- Probability: I start with $64 and bet half of my money on a coin flip six times. If I win three times and lose three times, how much do I gain or lose?
- Probability: An auto insurance company knows that unsafe drivers have a 40% chance of having an accident in a year, while safe drivers have only a 10% chance. If 85% of drivers are safe and the company observes an accident, what is the probability that the driver is unsafe?
- Probability: A jar contains 7 red balls and 10 black balls. If four balls are drawn without replacement, what is the probability that the first two are red and the last two are black?
- Probability: A closet contains 5 pairs of shoes. What is the probability of randomly selecting 5 shoes such that none form a complete pair?
- Probability: What is the probability of drawing a pair from a deck of cards when drawing the first two cards?
- Probability: You and a friend play a coin flip game. If the sequence “HH” appears first, you win; if “TH” appears first, your friend wins. What is your probability of winning this game?
- Probability: In a horse race with 8 horses, what is the probability that horse number 4 comes in second and horse number 1 finishes in the top three?
- Probability: We are flipping a fair coin. If heads, I score a point; if tails, you score a point. We continue flipping until one of us reaches three points. What is the expected score of the loser?
- Probability: What is the probability that the sum of three dice is 14?
- Combinatorics: A person has 9 friends and will invite 6 to a party. If two friends do not get along and cannot attend together, how many possible combinations of invitations are there?
- Combinatorics: How many unique circular bracelets can be made with 3 red beads and 3 green beads?
- Probability: What is the probability of being dealt a “Blackjack” (drawing two cards without replacement, one being a 10 to King and the other an Ace)?
- Combinatorics: How many palindromic arrangements exist for the word “MISSISSIPPI”?
- Probability: A small university offers three majors: Computer Science, Mathematics, and Philosophy. 50% of students major in Mathematics, 60% in Computer Science, and 20% in Philosophy; 6% major in all three. What percentage of students major in exactly two fields?
- Probability: An energy company is drilling for oil, with a 35% success rate and a 65% failure rate. If they find oil, the stock is worth $100; if they fail, it’s worth $16. The current stock price is $58.50. You have the right to buy the stock for $70 the day after they learn the outcome. What is the fair value of this right?
- Probability: I want to throw a party this weekend but worry about rain (70% chance on Saturday, 60% on Sunday). I will choose to have the party on the first sunny day. Fast forward to Monday, my friends loved the party. What is the probability that the party was on Saturday?
- Probability: If two squares are randomly selected from an 8x8 chessboard, what is the probability that the squares share the same row or column?
- Probability: I drew two cards without replacement from a standard deck of 52 cards, and they were a pair of 8s. I now plan to draw two more cards. What is the probability that the next two cards are also a pair?
- Probability: I have a bag with 3 red balls and 5 black balls. I will draw balls without replacement, one by one. What is the probability of drawing the last red ball by the fifth draw?
- Probability: I have a shuffled deck of cards and keep flipping until I reveal the first Ace, which is the 33rd card. What is the probability that the next card is the 7 of Diamonds? (The answer is not 1/51)
- Probability: You observe a candy conveyor belt and notice that for every five chocolates, four are followed by a soft-centered candy, and for every three soft-centered candies, two are followed by a chocolate. What fraction of the candies on the conveyor belt are soft-centered candies?
- Probability: You and a friend will play a coin flip game. If three heads appear consecutively first, you win; if four tails appear consecutively first, your friend wins. What is your probability of winning this game?
- Probability: A box contains 3 large donuts and 9 small donuts. Every hour, Homer randomly selects a donut from the box. If it’s a small donut, he eats it; if it’s a large donut, it’s cut in half, one half is eaten, and the other half is returned as a small donut. How many hours until only small donuts remain in the box?
Tips & Insights
- Focus on understanding probability and combinatorial concepts thoroughly, as many questions revolve around these topics.
- Practice solving problems under time constraints to improve speed and accuracy.
- Familiarize yourself with common probability distributions and their applications.