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:

Allowance Account

An account used to adjust the carrying value of accounts receivable to the amount expected to be collected.

Contra Account

An account used in conjunction with another account to adjust or offset its balance.

Allowance Account

An account set aside to cover potential losses from doubtful accounts, reflecting estimated uncollectible receivables.

Statement of Financial Position

A financial report detailing a company's assets, liabilities, and equity at a specific point in time, commonly known as a balance sheet.