A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to during the current year. In addition, it estimates that 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)

a)

And if we solve for we got:

And that represent the probability of the employees will experience lost-time accidents in both years and in percentage is 0.9%

b)

And replacing we got:

And in % would be 10.1 %

Step-by-step explanation:

Assuming the following question:

Company studied the number of lost-time accidents occurring at its Brownsville, Texas,  plant. Historical records show that 6% of the employees suffered lost-time 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 employees 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?

For this case we define the following events:

A= Represent the case last year

B= Represent the current year

We know the following probabilities from the problem:

We also know the following conditional probability:

Using the conditional probability definition from Bayes we know that:

And if we solve for we got:

And that represent the probability of the employees will experience lost-time accidents in both years and in percentage is 0.9%

b. What percentage of the employees will suffer at least one lost-time accident over the  two-year period?

For this case we can find this probability with

And using the total probability rule defined by:

And replacing we got:

And in % would be 10.1 %

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.