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

question 131

Short Answer

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.
​ $P \left( X \mid Y _ { 1 } \right) = 0.2$ , $P \left( X \mid Y _ { 2 } \right) = 0.2$ , $P \left( X \mid Y _ { 3 } \right) = 0.6$ , $P \left( Y _ { 1 } \right) = 0.3$ , $P \left( Y _ { 2 } \right) = 0.4$ .
​
Find $P \left( Y _ { 1 } \mid X \right)$ .
​ $P \left( Y _ { 1 } \mid X \right) =$ __________

---

Definitions:

Marginal Cost

The price required to create one more unit of a particular good or service.

Profits

The excess of revenues over costs and expenses in a business or economic transaction.

Price Elasticity

A measure in economics to show how the quantity demanded of a good or service responds to a change in its price.

Marginal Cost

The additional expenditure required to produce one more unit of a product or service.