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In a certain industry, 60 percent of all labor-management disputes are over wages, 15 percent are over working conditions, and 25 percent are over fringe issues. In addition, 45 percent of the disputes over wages are resolved without strikes, 70 percent of the disputes over working conditions are resolved without strikes, and 40 percent of the disputes over fringe issues are resolved without strikes.

1. What is the probability that a labor-management dispute in this industry will be resolved without a strike?

2. What is the probability that if a labor-management dispute in this industry is resolved without a strike, it was over wages? (Use Bayes’ Rule)

Answer :

1. The probability that a labor-management dispute in this industry will be resolved without a strike is 0.475 or 47.5%.

2. The probability that if a labor-management dispute in this industry is resolved without a strike, it was over wages is approximately 0.5684 or 56.84%.

To solve these questions, we can use the information given and apply basic probability concepts.

Let's denote:

- W: Dispute over wages

- C: Dispute over working conditions

- F: Dispute over fringe issues

- S: Dispute resolved without a strike

1. To find the probability that a labor-management dispute will be resolved without a strike, we need to calculate P(S), the probability of resolving a dispute without a strike.

P(S) = P(S|W) × P(W) + P(S|C) × P(C) + P(S|F) × P(F)

Given information:

- P(S|W) = 45% (45 percent of disputes over wages are resolved without strikes)

- P(S|C) = 70% (70 percent of disputes over working conditions are resolved without strikes)

- P(S|F) = 40% (40 percent of disputes over fringe issues are resolved without strikes)

- P(W) = 60% (60 percent of all labor-management disputes are over wages)

- P(C) = 15% (15 percent of all labor-management disputes are over working conditions)

- P(F) = 25% (25 percent of all labor-management disputes are over fringe issues)

Plugging in the values:

P(S) = 0.45 × 0.60 + 0.70× 0.15 + 0.40 × 0.25

= 0.27 + 0.105 + 0.1

= 0.475

Therefore, the probability that a labor-management dispute in this industry will be resolved without a strike is 0.475 or 47.5%.

2. To find the probability that if a labor-management dispute is resolved without a strike, it was over wages, we need to calculate P(W|S), the probability of a dispute being over wages given that it was resolved without a strike. We can use Bayes' rule to calculate this.

P(W|S) = (P(S|W) × P(W)) / P(S)

Using the values already known:

P(W|S) = (0.45 × 0.60) / 0.475

= 0.27 / 0.475

≈ 0.5684

Therefore, the probability that if a labor-management dispute in this industry is resolved without a strike, it was over wages is approximately 0.5684 or 56.84%.

Learn more about Bayes' rule here:

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