Problem 3: A certain factory operates three different shifts. Over the last year

Question

Problem 3: 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 Environments Unrelated to Environments 8% 10% 5% 35% 20% 22% Day Shift Swing Night 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 occurred on the day shit. (b) Compute the probability that the selected accident did not occur on the day shift. (c) If the selected accident was attributes to unsafe environments, then compute the probability that it occurred on the day shift.

Explanation / Answer

(a) Prob. = 0.08 + 0.35 = 0.43 = 43%

(b) Prob. = 1 - 0.43 = 0.57 = 57%

(c) Prob. = 0.08/(0.08 + 0.1 + 0.05) = 0.3478 = 34.78%

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