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 transient psychotic disorders (ATPD), those with “positive” schizophrenia (PS), and those with bipolar schizo-affective disorder (BSAD):

Personality Type ATPD (1) PS (2) BSAD (3) Total Obsessoid (O) 9 2 6 17 Asthenic=low Self-confident (A) 20 17 15 52 Asthenic=high Self-confident (S) 5 3 8 16 Nervous=tense (N) 474 15 Undeterminable (U) 4 13 9 26 Total 42 42 42 126 Source: Frank Pillmann, Raffaela Bloink, Sabine Balzuweit, Annette Haring, and Andreas Marneros, “Personality and Social Interactions in Patients with Acute Brief Psychoses,” Journal of Nervous and Mental Disease, 191 (2003), 503–508.

Find the following probabilities if a subject in this study is chosen at random:

(a) P(O)

(b) P Að Þ [ 2

(c) P(1)

(d) Pð Þ A

(e) P Að Þ j 3

(f) P 3Þð (g) Pð Þ 2 \ 3 (h) Pð Þ 2 j A