Question #40367

This question tests the application of De Morgan's Laws in probability and the danger of assuming independence for events defined on a shared sample space without replacement.

Students often attempt to calculate $P(A \cup B)$ using the inclusion-exclusion principle $P(A) + P(B) - P(A \cap B)$.

While $P(A)$ and $P(B)$ are straightforward, calculating $P(A \cap B)$ is complex.

A common lethal mistake is assuming the events 'sum is even' and 'product is divisible by 3' are independent, leading to the incorrect subtraction of $P(A)P(B)$ and the trap answer $487/630$.

The optimal blueprint bypasses this by transforming the union into a set complement $1 - P(A' \cap B')$, where the intersection of the complements is highly structured and easily countable.