The first is a is a sequence of problems that involve “coin tossing”, sometimes with very strange coins (like in part 3 below). If you are wondering, you could realize such “coins” by three entangled quantum electron-spins (often called entangled quantum bits or qubits). Entangled qubits are a key ingredient in quantum computation. In a similar fashion, while we talk of coin tosses, we are actually thinking of binary state physical systems that could settle in each state with certain probabilities. All quantum states are inherently probabilistic, and a lot of quantum mechanics tracks these probabilities. Indeed, what you learn in 342 and 345 is basically the axiomatic foundation of quantum mechanics.
Consider three coin tosses (imagine each coin shows Heads or Tails). At this stage, can you write the sample space? Probabilities? How many distinct events do you have?
Suppose the coin tosses are fair and every sequence of coin tosses has equal probability. What is the probability assignment for this model?
Instead, suppose we have a special coin, which we will call the Zero-Parity coin. If you toss the coin thrice, you will only see an even number of Heads among the toss outcomes (you will never see 3 Heads for example). In addition, each sequence with an even number of Heads has equal probability (whether the sequence has 0 or 2 Heads among 3 coin tosses). What is the probabilty assignment for this model?
Under each of the probability models, what is the probability we observe 2 Heads?