in the contract

Question

In contract negotiations, between a local govenment agency and its works, 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: What is the probability that an agreement will be reached on both issues

Answer 1

Using probability rules:

GIven:

P(S) = 0.5

P(I) = 0.7

P(not (S or I)) = 0.2

Using complement rule:

P(S or I) = 1 - 0.2 = 0.8

Rule for computing either or both

P(S or I) = P(S) + P(I) - P(S and I)

substituting:

0.8 = 0.5 + 0.7 - P(S and I)

0.4 = P(S and I) ---- agreement on both sides

Answer 2

Mark M. is correct!

In addition you will need to remember that

P(A or B) = P(A) + P(B) - P(A and B)

and that

P(A or B) + P[not (A or B)] = 1