A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 5% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employee will experience a lost-time accident in both years (to 1 decimal) ?

Question

Jamar Velazquez

Mathematics

22 November, 03:29

A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 5% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employee will experience a lost-time accident in both years (to 1 decimal) ?

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Sandra Avery · Answer 1

The percentage of the employee will experience a lost-time accident in both years is 0.0%

Step-by-step explanation:

Let A denote events that employees suffered lost-time accidents during the last year

Let B denote events that employees suffered lost-time accidents during the current year

P (A) = 5% = 0.05

P (B) = 4% = 0.04

P (B | A) = 15% = 0.15

(a) P (A ∩ B) = P (B | A) * P (A)

= 0.15 * 0.05

= 0.0075

= 0.0 (1 decimal place)

The probability that an employee will experience a lost - time accident in both years is 0.0