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

question 49

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.
$P \left( X \mid Y _ { 1 } \right) = 0.4$ , $P \left( X \mid Y _ { 2 } \right) = 0.5$ , $P \left( X \mid Y _ { 3 } \right) = 0.7$ , $P \left( Y _ { 1 } \right) = 0.7$ , $P \left( Y _ { 2 } \right) = 0.1$ .

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

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Definitions:

μs

The symbol for the population mean in statistics, representing the average value of a distribution.

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis, assuming the alternative hypothesis.

Analytical Comparison

The process of examining similarities and differences between two or more items or datasets to draw conclusions.

Critical Value

A threshold in hypothesis testing that determines the boundary between accepting or rejecting the null hypothesis.