During bad economic times, industrial workers are dismissed and are often replac

Question

During bad economic times, industrial workers are dismissed and are often replaced by machines. The history of 100 workers whose loss of employment is attributable to technological advances is reviewed. For each of these individuals, it was determined if he or she was given an alternative job within the same company, found a job with another company but is working in the same field, found a job in a new field, or has been unemployed for 1 year. In addition, the union status of each worker is recorded The following table summarizes the results. (a) If the selected workers found a job with a new company in the same field, what is the probability that the worker is a union member? (b) If the worker is a union member, what is the probability that the worker has been unemployed for a year?

Explanation / Answer

Ans:

a) P(New company same field)=0.23

P(union member/New company same field)=P(union member and New company same field)/P(New company same field)

=0.13/0.23

=0.5652

b)P(union member)=0.59

P(unemployed for a year/union member)=P(unemployed for a year and union member)/P(union member)

=0.02/0.59

=0.0339

Union Non Union Total Same Company 40 15 55 New Company(same field) 13 10 23 New field 4 11 15 Unemployed 2 5 7 Total= 59 41 100 Joint probability distribution Union Non Union Total Same Company 0.4 0.15 0.55 New Company(same field) 0.13 0.1 0.23 New field 0.04 0.11 0.15 Unemployed 0.02 0.05 0.07 Total= 0.59 0.41 1

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