I am wondering why in this case we don’t just do P(A) * P(B) = 0.4 * 0.5 = 0.2 to find the P(both). Is it because the question does not specify that these are independent events?
This. It could be, but it doesn’t have to.
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Thanks! I have a follow-up question. While the scenario when the two events don’t overlap at all is called mutually exclusive, is everything else where they overlap slightly to fully independent events? What do we call the case when they fully overlap ?
Independent events generally overlap, but that is just one overlap case. In other words, just because something overlaps does not mean that they have to be independent, but if something is independent, it must overlap (unless one of the events have zero probability).
Complete overlap.