(Solved): Cryptography 4. Probability [20 marks] Consider the following two experiments: - Experiment 1: Alic ...

Cryptography

4. Probability [20 marks] Consider the following two experiments: - Experiment 1: Alice flips a fair coin (0.5 probability of getting HEADS and \( 0.5 \) for TAILS), and shares the result with Bob. - Experiment 2: Alice flips a fair coin, and always sends HEADS to Bob. After each experiment, Bob needs to guess which experiment they were in. We can quantify the quality of Bob's guess using the following formula: \[ Q=\left|P\left(W_{1}\right)-P\left(W_{2}\right)\right| \] Here \( W_{i} \) refers to the event that Alice performed experiment \( i(i \in\{1,2\}) \), while Bob guessed they were in experiment 1 . We can see that \( Q=0 \) indicates Bob cannot distinguish the two experiments, while \( Q=1 \) suggests Bob can always correctly identify