The Journal of Economic Psychology (Sept. 2008) published the results of a high-stakes experiment where subjects were asked how much they would pay for insuring a valuable painting. The painting was threatened by fire and theft, hence the need for insurance. To make the risk realistic, the subjects were informed that if it rained on exactly 24 days in July, the painting was considered to be stolen; and, if it rained on exactly 23 days in August, the painting was considered to be destroyed by fire. Although the probability of these two events, “fire” and “theft,” was ambiguous for the subjects, the researchers estimated their probabilities of occurrence at .0001. Rain frequencies for the months of July and August were shown to follow a Poisson distribution with a mean of 10 days per month.
a. Find the probability that it will rain on exactly 24 days in July.
b. Find the probability that it will rain on exactly 23 days in August.
c. Are the probabilities, parts a and b , good approximations to the probabilities of “fire” and “theft”?