Experience has shown that 60% of the time a strike by union workers is settled within two-weeks

Question

Experience has shown that 60% of the time a strike by union workers is settled within two-weeks; 55% of the time the union strike fund is adequate to support a strike; and 40% of the time both conditions are satisfied. What is the probability of a strike settlement given that you know the union's strike fund to be adequate to support a strike? Is the settlement of a strike within a two-week period dependent on whether the strike fund if adequate

Answer 1

Let's call Event A, the strike is settled within 2 weeks, then Event A^c  is that the strike is not settled in two weeks.

Likewise, Event B is the union strike fund is adequate and Event B^C is that the union strike fund is not adequate.

Note that Probability of Event A + Probability of A^C = 1; and  Probability of A^C = 1- Probability(A)

 

Probability of Event A = .6

Probability if Event B = .55

Probability of A and B = .40

 

The problem asks: given that union strike fund is adequate, what is the probability that strike is settled within two weeks

 

This is called conditional probability or P(A|B) = P(A&B)/P(B) = .4/.55 = .7273

 

The events are independent if P(A|B) = P(A)

 

Since P(A|B) = .7273 does not equal P(A) = .6,  they are not equal and therefore the settlement of a strike within two weeks is dependent upon the strike fund being adequate.