Question

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.

Answer 1

The probability of reaching an agreement on both salaries and insurance benefits is 35%. The agreement on salaries and insurance benefits is not independent.

Step-by-step explanation:

Part A: To find the probability that an agreement will be reached on both issues, we multiply the probabilities of reaching an agreement on salaries and insurance benefits. Therefore, P(A and B) = P(B|A) * P(A), which is equal to (0.70) * (0.50) = 0.35 or 35%.

Part B: To determine if the agreement on salaries and insurance is independent, we compare P(B) and P(B|A). If they are equal, then the events are independent. However, P(B) = 0.70 and P(B|A) = 0.85, which are not equal. Therefore, the agreement on salaries and insurance is not independent.

Answer 2

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:

`P(Agreement)=(400)/(1000)\\\\\\=0.4`

b. To determine whether the two events are independent, we compare the probabilities
`P(s)* P(i)` and
`P(s \ and \ i)` where i denotes insurance and s denotes salaries:

`P(s)* P(i)=0.5* 0.7\\\\=0.35\\\\\\P(s \ and \ i)=0.4`

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

`P(A).P(B)=P(A\ and \ B)\\\\=>P(s).P(i)\\eq P(s\ and\ i)`

Hence, the events are not independent.