Do people estimate combined probabilities differently to uncombined ones? Suppose, somebody has to estimate the likelihood of one of the following events (or has to estimate which event is more likely):


A coin is tossed six times and each time the result is heads. (combined)
A 64-sided die is rolled and the result is 1. (uncombined)


Since 2⁶ = 64, both events are obviously equiprobable. However, somebody with less statistical prowess might think otherwise. Also, in a more complex scenario (e.g., in a board game) at least one of the probabilities may be impossible to calculate for almost anybody (at least in a short time).

I am interested in studies that investigate, whether combined probabilities (1) are estimated to be higher, lower or equal than uncombined probabilities (2), even if the actual probabilities are identical.

I am also interested in studies, which investigate the influence of the presentation of the scenario on the estimation of probabilities: Is the same scenario perceived differently, if presented in a way that emphasises combinedness? For example, one could simply ask somebody to estimate the probability that one of his close relatives will die within a year (uncombined) or one could ask him to list all his close relatives, their age and state of health first (combined). After all, a lot of probabilities with real-life applications are combined.

Note that I am not interested in which of the estimates is more accurate, only which one is higher.
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.