Last lesson ended with a warning: P(A and B) = P(A) · P(B) — multiplying the plain, unconditional probabilities — is only legal when A and B are independent. Time to make that precise.
Two events are independent when learning that one happened doesn’t move your probability of the other at all:
P(A | B) = P(A)
Plug that into the multiplication rule P(A and B) = P(A | B) · P(B) and the conditional collapses: P(A and B) = P(A) · P(B). So “multiply the plain probabilities” isn’t a separate rule — it’s the multiplication rule in the special case where conditioning changes nothing.
Note what independence is not: it is not “the events feel unrelated,” “the events are physically separate,” or “nobody planned a connection.” It’s a claim about information: knowing B leaves your belief about A exactly where it was. That’s a strong claim, and the world violates it constantly — most often through a common cause lurking behind both events.
Each option in the question multiplies two per-event probabilities to get a joint. Three of the multiplications are fine. One of them is the kind of error that has produced real disasters — in datacenters and in courtrooms.