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Chapter 2: Problem 20

A certain factory operates three different shifts. Over the last year, 200 accidents have occurred at the factory. Some of these can be attributed at least in part to unsafe working conditions, whereas the others are unrelated to working conditions. The accompanying table gives the percentage of accidents falling in each type of accidentshift category. $$ \begin{array}{llcc} & & \begin{array}{c} \text { Unsafe } \\ \text { Conditions } \end{array} & \begin{array}{c} \text { Unrelated } \\ \text { to Conditions } \end{array} \\ \hline \text { Shift } & \text { Day } & 10 \% & 35 \% \\ & \text { Swing } & 8 \% & 20 \% \\ \text { Night } & 5 \% & 22 \% \\ \hline \end{array} $$ Suppose one of the 200 accident reports is randomly selected from a file of reports, and the shift and type of accident are determined. a. What are the simple events? b. What is the probability that the selected accident was attributed to unsafe conditions? c. What is the probability that the selected accident did not occur on the day shift?

Short Answer

Expert verified
a. Day-Unsafe, Day-Unrelated, Swing-Unsafe, Swing-Unrelated, Night-Unsafe, Night-Unrelated. b. 0.23 c. 0.55

Step by step solution

01

Identify Simple Events

We are given a table that categorizes accidents by shift and type of accident. The simple events are combinations of shifts (Day, Swing, Night) and accident types (Unsafe Conditions, Unrelated to Conditions). We have six simple events: 1) Day-Unsafe, 2) Day-Unrelated, 3) Swing-Unsafe, 4) Swing-Unrelated, 5) Night-Unsafe, 6) Night-Unrelated.
02

Calculate Probability for Unsafe Conditions

To find the probability of an accident due to unsafe conditions, calculate the total accidents attributed to this cause. Sum the percentages of unsafe conditions over all shifts: Day (10%), Swing (8%), Night (5%). Total = 10% + 8% + 5% = 23%. Since there are 200 accidents, the probability is 0.23.
03

Calculate Probability for Non-Day Shift Accidents

To find the probability of an accident not occurring on the day shift, sum the percentages of accidents from swings and nights (both types of conditions): Swing-Unsafe (8%), Swing-Unrelated (20%), Night-Unsafe (5%), Night-Unrelated (22%). Total = 8% + 20% + 5% + 22% = 55%. Therefore, the probability is 0.55.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simple Events
In probability, a simple event is the most basic possible outcome of a particular experiment or situation. For this exercise, we're looking at a factory where accidents are categorized by the type of accident and the shift during which they occur. The given table divides accidents by two criteria: the shift (day, swing, and night) and the nature of the accident (unsafe conditions vs. unrelated to conditions). Each unique combination of shift and accident type represents a simple event.
  • Day-Unsafe: Accidents on the day shift attributed to unsafe conditions.
  • Day-Unrelated: Accidents on the day shift not related to working conditions.
  • Swing-Unsafe: Accidents on the swing shift attributed to unsafe conditions.
  • Swing-Unrelated: Accidents on the swing shift not related to working conditions.
  • Night-Unsafe: Accidents during the night shift attributed to unsafe conditions.
  • Night-Unrelated: Accidents during the night shift not related to working conditions.
These simple events provide a comprehensive framework to analyze the probability of each type of accident occurring at the factory.
Probability Calculation
Probability is a measure of the likelihood of an event occurring and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In the context of this factory scenario, we're given percentages for different types of accidents occurring during different shifts. To find the probability of an accident being attributed to unsafe conditions, you sum the percentages of such accidents across all shifts (10% for day, 8% for swing, 5% for night) and convert that total into a probability.
  • Total Unsafe: 10% + 8% + 5% = 23%
  • Probability: Since there are 200 total accidents, the probability of selecting an unsafe condition accident is 0.23 (or 23%).
For the case of accidents that did not occur on the day shift, you add up the percentages for swing and night shifts accidents (both unsafe and unrelated). This calculation encompasses all accidents that happened outside of the day shift.
  • Swing and Night (All Types): 8% + 20% (swing) + 5% + 22% (night) = 55%
  • Probability: Thus, the probability is 0.55 (or 55%) for an accident not happening on the day shift.
Shift Work Accidents
Shift work can often contribute to the varying risk of workplace accidents. The time of day, worker fatigue, and shift length all influence the probability of accidents occurring. In this scenario, the breakdown provided in the table highlights how shifts can be associated differently with accident risks, whether due to unsafe conditions or factors unrelated to conditions. Understanding how shift work affects safety helps in managing risks and tailoring safety measures accordingly. For instance, knowing that a significant proportion of accidents occur during swing or night shifts could point to higher fatigue levels among workers or decreased supervision during nighttime hours. It鈥檚 important to:
  • Continuously monitor accident rates by shift to identify patterns or problems.
  • Adjust working conditions or schedules to mitigate risks, such as implementing more breaks or rotating shifts to minimize fatigue.
  • Enhance training for safety practices specifically tailored to each shift type.
Evaluating these patterns helps organizations plan more effectively to reduce accidents regardless of shift configurations. By understanding the dynamics of shift work accidents, companies can undertake proactive steps to create a safer work environment.

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Most popular questions from this chapter

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