Answer to Question #145635 in Statistics and Probability for qwerty

Question

3. Factory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur due to carelessness or so-called human error. In addition, the worker's shift, 7:00 AM - 3:00 PM (day shift), 3:00 PM - 11:00 PM (evening shift), or 11:00 PM - 7:00 AM (graveyard shift), may be a factor. During the last year, 300 accidents have occurred. The percentages of the accidents for the condition combinations are as shown in the table below. If an accident report is selected randomly from the 300 reports,
SHIFT UNSAFE HUMAN
CONDITION ERROR
DAY 5% 32%
EVENING 6% 25%
GRAVEYARD 2% 30%
(a) what is the chance that the accident occurred on the evening shift?
(b) what is the chance that the accident occurred on either the day or the graveyard shift?
(c) what is the chance that the accident did not happen in the graveyard shift?

Answer 1

During the last year, 300 accidents have occurred. The percentages of the accidents for the condition combinations are

a) The chance that the accident occurred on the evening shift is

$$\frac{31}{100}=0.31$$

b) The chance that the accident occurred on either the day or the graveyard shift is

P(the accident occurred on either the day or the graveyard shift) = P(the accident occurred on the day shift) + P(the accident occurred on the graveyard shift)

$$\frac{37}{100}+\frac{32}{100}=\frac{69}{100}=0.69$$

Or:

P(the accident occurred on either the day or the graveyard shift) = 1 – P(the accident occurred on the evening shift)

$$1-0.31=0.69$$

c) The chance that the accident did not happen in the graveyard shift?

P(the accident did not happen in the graveyard shift) = 1 – P(the accident happened in the graveyard shift)

$$1-\frac{32}{100}=0.68$$

Answer:

a) 0.31

b) 0.69

c) 0.68