A company studied the number of lost time accidents...

A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 10% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 3% 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)? Answer= 1.5% b. What percentage of the employee will experience a lost-time accident over the two-year period (to 1 decimal)?

Transcript

00:01 Okay, we're told that in a given factory setting or something like that, 1 % or sorry, 10 % of employees last year experienced some kind of accident.

00:12 And this year, management believes they can get it down to 3 % of employees suffering an accident within this past year, or like in this coming year.

00:23 And so i've created this chart here, which shows, did the employee experience an accident last year? yes or no, and did the employee experience an accident this year, yes or no? so we know the total percentage of employees who will experience an accident this year is 0 .03 or 3%.

00:42 And the total number of employees who experienced an accident last year is 0 .1 or 10%.

00:48 We're also know that out of the employees who experienced an accident last year, 15 % will experience when this year.

00:57 So again, the probability of having one this year, given the experience when last year is equal to 0 .15.

01:01 We also know that conditional probability is equal to the probability that both events will happen divided by the probability of the condition.

01:13 So the probability of someone experiencing an accident this year, given that they experienced one last year, is equal to 0 .15.

01:22 And this is equal to the probability they'll experience one both years, divided by the probability that they'll experience one last year.

01:31 And we know that last year, 10 % of employees experienced an accident.

01:37 So this is equal to 0 .1.

01:39 So 0 .15 times 0 .1 is equal to the overlap of the two or the percentage of employees who experienced one both years.

01:47 So this is going to be 0 .015 percent of employees experienced one both years.

01:54 As a result, because these have to add up to 1, that means that 0 .085 percentage...

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