5. Pillman et al. (A-11) studied patients with acute brief episodes of psychoses. The researchers classified subjects into four personality types: obsessiod, asthenic/low self-confident, asthenic/high self-confident, nervous/tense, and undeterminable. The table below cross- classifies these personality types with three groups of subjects those with acute and tran- sient psychotic disorders (ATPD), those with "positive" schizophrenia (PS), and those with bipolar schizoaffective disorder (BSAD): Personality Type Obsessoid (0) ATPD (1) PS (2) BSAD (3) Total Asthenic/low Self-confident (4) 20 Asthenic high Self-confident (S) Nervous/tense (N) Undeterminable (U) Total 13 42 42 2 17 17 15 52 16 15 26 42 126 SOURCE: Frank Fillmann, Raffeela Bloiak, Sabine Balzuweit, Annette Haring, and Andreas Manema, "Personality and Social Interactions in Patients with Acute Brief Psychoses," The Journal of Nervous and Mental Disease, 191 (2003), 503-500. Find the following probabilities if a subject in this study is chosen at random:

(b) PAU2)

(c) P(1)

(a) P(O)

(e) P(A|3)

(f) P(3)

(d) P(A) (g) P(23) (h) P(2|A)