the question goes as follows:

Medical case histories indicate that different illnesses may produce identical symptoms. Suppose that a particular set of symptoms, denoted , occurs only when one of the tress illnesses, occurs. Assume that the simultaneous occurrence of more ten one of these illnesses is impossible and that

in addition:

assuming that an ill person exhibits the symptoms, , what is the probability that the person has illness ?

solution:

To find

so

therefore:

is this correct, or am I missing something?