1 Interview brainteasers 1 2 Interview brainteasers 2 3 Interview brainteasers 3 4 Interview brainteasers 4 5 Combinatorial geometry 6 Multiplayer games

# Brainteasers from Interviews - Part 3

#### 150 Most Frequently Asked Questions on Quant Interviews

by Dan Stefanica, Rados Radoicic, and Tai-Ho Wang, second edition, FE Press 2019, 281 pages

#### Probability and Stochastic Calculus Quant Interview Questions

by Ivan Matic, Rados Radoicic, and Dan Stefanica, FE Press 2021, 334 pages

#### Challenging Brainteasers for Interviews

by Rados Radoicic, Ivan Matic, and Dan Stefanica, FE Press 2023, 345 pages

Problem 1. There are $$M$$ green apples and $$N$$ red apples in a basket. We take apples out randomly one by one until all the apples left in the basket are red. What is the probability that at the moment we stop the basket is empty?

Problem 2. If $$x_1, x_2, \ldots, x_9$$ is a random arrangement of numbers $$1$$, $$2$$, $$\ldots$$, $$9$$ around a circle, what is the probability that $$\sum_{i=1}^{9} \left|x_{i+1} - x_i\right|$$ is minimized? (Here, $$x_{10} = x_1$$.)

Problem 3. There are $$1000$$ green balls and $$3000$$ red balls in container $$A$$, and $$3000$$ green balls and $$1000$$ red balls in container $$B$$. You take half of the balls from $$A$$ at random and transfer them to $$B$$. Then you take one ball from $$B$$ at random. What is the probability that this ball is green?

Problem 4.

A robot performs coin tossing. It is poorly designed, it produces a lot of sounds, lights, and vapors, and it takes one hour to toss a coin. Yet in the end, when the coin finally lands, it somehow has equal probability of showing heads and tails.

Two scientists, $$A$$ and $$B$$, enjoy observing this robot and, by analyzing its unusual and faulty behavior, they became fairly decent at guessing whether the coin will land heads or tails half an hour before the coin is released from the robot's hand. The scientist $$A$$ has $$80\%$$ chance of successfully predicting the outcome, while the scientist $$B$$ is successful $$60\%$$ of the time.

The robot started its routine, and the scientist $$A$$ predicts the coin will land tails. The scientist $$B$$ predicts the coin will land heads. Can you calculate the probability that the coin will land heads?

Problem 5. A player chooses a number $$k \le 52$$ and the top $$k$$ cards are drawn one by one from a properly shuffled standard deck of $$52$$ cards. The player wins if the last drawn card is an Ace and if there is exactly one more Ace among the cards drawn. Which $$k$$ should the player choose to maximize the chance of winning in this game?