Please see the image below: Routine physical examinations are conducted annually

Question

Please see the image below:

Routine physical examinations are conducted annually as part of a health service program for General Concrete Inc. employees. It was discovered that 16% of the employees need corrective shoes, 30% need major dental work, and 7% need both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work? (5pts) If 7% need both corrective shoes and major dental work, what is the probability that neither corrective shoes nor dental work are needed. Show your calculations using the complement rule. (5pts) In words, explain the part of the Venn Diagram that shows the answer to (a) and then explain the answer to (b). What color and shape do they represent in the Venn Diagram. (5 pts) a. b. c.

Explanation / Answer

a) let A is event of employee need corrective shoes and event B is they need major dental work

therefore P(either corrective shoes or major dental work)=P(A U B)=P(A)+P(B)-P(A n B) =0.16+0.30-0.07=0.39

b)

P(neither corrective nor dental work is required) =1-P(A U B) =1-0.39 =0.61

c)

here part A represent employee need corrective shoes

and part B represent employee need major dental work

Blue color represent event B in above whcih represent neither A nor B.

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