Pillman et al. (A-11) studied patients with acute brief episodes of psychoses. T
ID: 3065913 • Letter: P
Question
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)
4
7
4
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(A U 2)
(c) P(1)
(d) P(A')
(e) P(A | 3)
(f) P(2 n 3)
(g) P (2 |A)
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)
4
7
4
15
Undeterminable (U)
4
13
9
26
Total
42
42
42
126
Explanation / Answer
We have been given stats
so
(a). P(O) = 17/126
(b). P(A U 2) = P(A) + P(2) - P(A n 2) = 52/126 + 42/126 -17/126 = 77/126
(c). P(1) = 42/126 = 1/3
(d). P(A') = (126 - 52)/126 = 74/126 = 37/63
(e). P(AI3) = P(A n 3)/P(3) = (6/126) /(42/126) = 6/42 = 1/7
(f). P(2 n 3) = 0/126 = 0 since they nothing in common
(g). P(2 I A) = P(2 n A)/P(A) = (17/126)/(52/126) = 17/52