Question

1. 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 environments, whereas the others are unrelated to working environments. The accompanying table gives the percentage of accidents falling in each type of accident–shift category.

Unsafe Environment Unrelated to Environment

Day 10% 30%

Swing 12% 21%

Night 5% 22%

Suppose one of the 200 accident reports is randomly selected from a file of report, and the shift and type of accident are determined.

a. Compute the probability that the selected accident was due, in part, to an unsafe environment.

b. If the selected accident occurred during a swing shift, compute the probability that it was, in part, due to an unsafe work environment.

c. If the selected accident was attributed to an unsafe environment, then compute the probability that it occurred on the night shift.

d. Is the cause of the accident (unsafe environment vs unrelated) dependent or independent of the Work Shift? Use numbers to argue your case.

Answer 1

(a)

From the given data,the following Table is calculated:

	Unsafe environment	Unrelated to environment	Total
Day Shift	0.10	0.30	0.40
Swing Shift	0.12	0.21	0.33
Night Shift	0.05	0.22	0.27
Total	0.27	0.73	1.00

P(Unsafe environment) = 0.27

So,

Answer is:

0.27

(b)

P(Unsafe environment/ Swing shift) = P(Unsafe environment AND Swing shift) / P(Swing shift)

= 0.12/0.33 = 0.3636

So,

Answer is:

0.3636

(c)
P(Night Shift/ Unsafe environment) = P(Night Shift AND Unsafe environment)/ P(Unsafe environment)

= 0.05/0.27 = 0.1852

So,

Answer is:

0.1852

(d)

P(Unsafe environment) = 0.27

P(Unrelated to environment) = 0.73

So

P(Unsafe environment) X P(Unrelated to environment) =0.27 X 0.73 = 0.1971

But,

P(Unsafe environment AND Unrelated to environment) = 0

Since P(Unsafe environment) X P(Unrelated to environment) = 0.1971 P(Unsafe environment AND Unrelated to environment) = 0, the cause of the accident (unsafe environment vs unrelated) are dependent of the Work Shift