1. | Interview brainteasers 1 |

2. | Interview brainteasers 2 |

3. | Interview brainteasers 3 |

4. | Interview brainteasers 4 |

5. | Combinatorial geometry |

6. | Multiplayer games |

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

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

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

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?