Use Bayes' Theorem or a Tree Diagram to Calculate the Indicated

question 88

Multiple Choice

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places. $Y _ { 1 }$ , $Y _ { 2 }$ , $Y _ { 3 }$ form a partition of S.
$P \left( X \mid Y _ { 1 } \right) = 0.2$ , $P \left( X \mid Y _ { 2 } \right) = 0.3$ , $P \left( X \mid Y _ { 3 } \right) = 0.6$ , $P \left( Y _ { 1 } \right) = 0.2$ , $P \left( Y _ { 2 } \right) = 0.4$ .

Find $P \left( Y _ { 1 } \mid X \right)$ .

• A) \(P \left( Y _ { 1 } \mid X \right) = 0.6\)
• B) \(P \left( Y _ { 1 } \mid X \right) = 0.9\)
• C) \(P \left( Y _ { 1 } \mid X \right) = 0.0072\)
• D) \(P \left( Y _ { 1 } \mid X \right) = 0.3\)
• E) \(P \left( Y _ { 1 } \mid X \right) = 0.1\)

---

Definitions:

Chronemics

The study of how time affects communication in different cultures, including time management, punctuality, and the structuring of time in interactions.

Body Language

Non-verbal communication through physical behaviors such as facial expressions, gestures, and posture.

Transactional Process Model

A theoretical framework suggesting communication is an interactive process involving simultaneous sending and receiving of messages.

Nonverbal Signals

Communication cues given through body language, facial expressions, and other physical behaviors rather than words.