Do people estimate combined probabilities differently to uncombined ones?
I believe these questions are dealt with by "support theory," the seminal publications being:


Tversky, A., &amp; Koehler, D. J. (1994). Support theory: A nonextensional representation of subjective probability. Psychological Review, 101(4), 547-566.
Rottenstreich, Y., &amp; Tversky, A. (1997). Unpacking, repacking, and anchoring: advances in support theory. Psychological review, 104(2), 406.


One of the basic findings accounted for by support theory is an unpacking effect whereby people judge an event that implicitly consists of a disjunction of many events (e.g., the probability that a person will "die from a natural cause") as less probable than the sum of the probability estimates for some component events that one could "unpack" the original hypothesis into (e.g., the sum of [a] the probability a person will die from heart disease, [b] the probability a person will die from cancer, [c] the probability a person will die from other natural causes). For example, in one study reported in Tversky &amp; Koehler (1994), participants on average judged the probability of the implicit disjunction above ("death from a natural cause") to be 58%, and the probability of the unpacked version to be 22% + 18% + 33% = 73%. In the words of Tversky &amp; Koehler, "unpacking an implicit disjunction may increase, but not decrease, its judged probability" (p. 549).

There is a lot more to support theory than just this unpacking effect, but a more complete summary of the theory is beyond my knowledge.