Question

Lost-Time Accidents. A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that $6 \%$ of the employees suffered losttime accidents last year. Management believes that a special safety program will reduce such accidents to $5 \%$ during the current year. In addition, it estimates that $15 \%$ of employets who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employees will experience lost-time accidents in both years? b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?

Name: Problem 57, Chapter 4: Essentials of Statistics for Business & Economics
Uploaded: 2023-12-02T17:30:36-08:00
Channel: Rashmi Sinha

   Lost-Time Accidents. A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that $6 \%$ of the employees suffered losttime accidents last year. Management believes that a special safety program will reduce such accidents to $5 \%$ during the current year. In addition, it estimates that $15 \%$ of employets who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?

Essentials of Statistics for Business & Economics

David R. Anderson;… 9th Edition

Chapter 4, Problem 57

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Solved by Expert Rashmi Sinha

12/02/2023

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Lost-Time Accidents. A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that $6 \%$ of the employees suffered losttime accidents last year. Management believes that a special safety program will reduce such accidents to $5 \%$ during the current year. In addition, it estimates that $15 \%$ of employets who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employees will experience lost-time accidents in both years? b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?

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Key Concepts

Conditional Probability

Conditional probability refers to the likelihood that an event will occur given that another event has already occurred. It’s a fundamental concept in probability that helps in determining the chance of outcomes when events are interdependent.

Intersection of Events

The intersection of events represents the scenario where two or more events occur simultaneously. In probability calculations, the probability of the intersection is often obtained by multiplying the probability of one event by the conditional probability of the second event occurring given the first.

Union of Events

The union of events denotes the probability that at least one of a set of events will occur. It typically involves adding the probabilities of the individual events and then subtracting the probability of their intersection to correct for any overlap in counting.

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