It is known from experience that in a certain industry 40 percent of all labour-management disputes are over wages, 40 percent are over working conditions, and 20 percent are over fringe benefit. Also, 9 percent of the disputes over wages are resolved without strikes, 20 percent of the disputes over working conditions are resolved without strikes, and 6 percent of the disputes over fringe benefit are resolved without strikes.
(i) What is the probability that a labour-management dispute in this industry will be
resolved without a strike?
(ii) What is the probability that a labour-management dispute is over working conditions if it is resolved without a strike?
To answer these questions, we can use conditional probability. Let's break down the information provided and solve each part.
(i) What is the probability that a labor-management dispute in this industry will be resolved without a strike?
To determine the probability of a labor-management dispute being resolved without a strike, we need to sum up the probabilities of all three types of disputes being resolved without strikes.
P(Resolved without strike) = P(Wage dispute resolved without strike) + P(Working conditions dispute resolved without strike) + P(Fringe benefit dispute resolved without strike)
From the information provided, we know that:
P(Wage dispute resolved without strike) = 9% = 0.09
P(Working conditions dispute resolved without strike) = 20% = 0.20
P(Fringe benefit dispute resolved without strike) = 6% = 0.06
Plugging these numbers into the formula:
P(Resolved without strike) = 0.09 + 0.20 + 0.06 = 0.35
Therefore, the probability that a labor-management dispute in this industry will be resolved without a strike is 0.35 or 35%.
(ii) What is the probability that a labor-management dispute is over working conditions if it is resolved without a strike?
To find this probability, we need to calculate the conditional probability using Bayes' theorem:
P(Working conditions dispute | Resolved without strike) = P(Working conditions dispute ∩ Resolved without strike) / P(Resolved without strike)
From the information provided, we know that:
P(Working conditions dispute resolved without strike) = 20% = 0.20
Therefore,
P(Working conditions dispute | Resolved without strike) = P(Working conditions dispute resolved without strike) / P(Resolved without strike)
= 0.20 / 0.35
≈ 0.5714
So, the probability that a labor-management dispute is over working conditions if it is resolved without a strike is approximately 0.5714 or 57.14%.