a) I'm not sure what answer is desired here, but based on his calculation of the probability of H3 being true, he is assuming that the hypotheses H1, H2, and H3 are mutually exclusive.
An experimenter observes the occurrence of an event A as the result of a particular experiment. There are three different hypotheses, H1, H2, and H3, which the experimenter regards as the only possible explanations of the occurrence of A. under hypothesis H1, the experiment should produce the result A about 10% of the time over the long run, under H2 about 1% of the time, and under H3 about 39% of the time. Having observed A, the experimenter decides that H3 is the most likely explanation, and that the probability that H3 is true is
39 %/( 10%+1%+39%) =78%
a)What assumption is the experimenter implicitly making?
b)Does the probability 78% admit a long-run frequency interpretation?
c)Suppose the experiment is a laboratory test on a blood sample from an individual chosen at random from a particular population. The hypothesis Hi is that the individual’s blood is of some particular type i. over the whole population it is known that the proportion of individuals with blood of type 1 is 50%, the proportion with type 2 blood is 45%, and the remaining proportion is type 3. Revise the experimenter’s calculation of the probability of H3 given A, so that is admits a long-run frequency interpretation. Is H3 still the most likely hypothesis given A?