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We can multiply the probabilities of individual die rolls because the rolls are assumed to be mutually independent events. For independent events A, B, and C, the probability that all occur is the product of their individual probabilities: $P(A \cap B \cap C) = P(A) \times P(B) \times P(C)$.

Conditions: The events (rolls) must be mutually independent.; Pairwise independence alone is not sufficient for the three-event product rule; mutual independence is required.; The multiplication rule applies to the intersection of independent events.

We can multiply the probabilities of individual die rolls because the rolls are assumed to be mutually independent events. For independent events A, B, and C, the probability that all occur is the product of their individual probabilities: $P(A \cap B \cap C) = P(A) \times P(B) \times P(C)$.

Conditions: The events (rolls) must be mutually independent.; Pairwise independence alone is not sufficient for the three-event product rule; mutual independence is required.; The multiplication rule applies to the intersection of independent events.