Question

You’re a human factors engineer at a large manufacturing facility that operates three shifts: day, swing, and night. In 2019, 200 accidents were reported, and you’ve parsed those out by (i) the shift in which they occurred and (ii) the cause of the accident, whether due to what you found to be unsafe conditions or unrelated to the conditions of the facility. The following table contains your accounting of the 200 accidents. You randomly draw one of the accidents at random to study.

Shift Unsafe conditions Unrelated to conditions

Day 20 70

swing . 16    40

night . 10     44

a. What is the probability that the accident was attributed to unsafe conditions?

b. What is the probability that the accident occurred in the Day or the Swing shifts?

c. What is the probability that the accident was due to unsafe conditions and occurred during the Night shift?

d. Given that the accident was unrelated to conditions at the facility, what is the probability that it occurred during the Swing shift?

Answer 1

	unsafe	unrelated					Total
day	20	70					90
swing	16	40					56
night	10	44					54
Total	46	154					200

a) P(unsafe conditions) = 46/200 = 0.23 or 23%

b) probability that the accident occurred in the Day or the Swing shifts = (90+56)/200 = 0.73 or 73%

c)  probability that the accident was due to unsafe conditions and occurred during the Night shift = 10/200 = 0.05 or 5%

d) P(swing shift | unrelated) = P(swing shift and unrelated) / P(unrelated) = 40/154=0.2597 or 25.97%