Question 11 A radioactive source is monitored for an hour and the number of detected emissions from it, denoted as, is counted. The source is known to be one of two substances A or B. If the source is A, then the theory says that the number of emissions should have a Poisson distribution with parameter 3.1 and the source is B , then the theory says that the number of emissions should have a Poisson distribution with parameter 4.9. It is known that the probability that the source is substance A is p. (a) Give the conditional probability that an. emissions are detected given that the source is substance A. (b) Give the (imconditional) probability that n emissions are detected. (c) Show that the conditional probability that the source is substance A given that in emissions are detected denoted p(A|n) is given by 1 MAI\") = - 1 + 7p\"? 1'8 (: (d) Determine also 10(Bln). Under which condition on p, MEI\") 2 MAI\") for all possible observations 11