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In contract negotiations between a local government agency and its workers,
it is estimated that there is a 50% chance that an agreement will be reached
on the salaries of the workers. It is estimated that there is a 70% chance that
there will be an agreement on the insurance benefits. There is a 20% chance
that no agreement will be reached on either issue.
Part A: Find the probability that an agreement will be reached on both
issues.
Part B: Based on your answer from Part A, determine whether the
agreement on salaries and the agreement on insurance are independent
events. Justify your answer.

Respuesta :

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Answer:

a. 0.4

b. Not independent.

Step-by-step explanation:

a. We use the probability table attached below for our calculations.

-the probability that an agreement is reached on both sides is obtained from the table:

[tex]P(Agreement)=\frac{400}{1000}\\\\\\=0.4[/tex]

b. To determine whether the two events are independent, we compare the probabilities [tex]P(s)\times P(i)[/tex] and [tex]P(s \ and \ i)[/tex] where i denotes insurance and s denotes salaries:

[tex]P(s)\times P(i)=0.5\times 0.7\\\\=0.35\\\\\\P(s \ and \ i)=0.4[/tex]

Two events are considered to be independent, if and only if:

[tex]P(A).P(B)=P(A\ and \ B)\\\\=>P(s).P(i)\neq P(s\ and\ i)[/tex]

Hence, the events are not independent.

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