A certain factory operates three diferent shifts. Over the last year, 200 accide

Question

A certain factory operates three diferent shifts. Over the last year, 200 accidents have occurred at the can be attributed at least in part to unsafe working conditions, whereas the others are unrelate Question Details these conditions. The eccompanying table gives the percentage of accidents falling in each type of accident-shift category Unsafe Unrelated Conditions to Conditions 29% 15% 33% Day 12% 7% 4% shift Swing Suppose one of the 200 accident reports is randomly selected from a file of reports, and the shift and type o determined o) What are the simple events? (Let S, S, and S, represent the day, swing, and night shifts, respectively. Let C and Co represent the unsafe conditions and unrelated to conditions, respectively. Enter your answer in set notation.) (b) What is the probability that the selected accident was attributed to unsafe conditions? e What is the probability that the selected accident did not occur on the day shift? Question Detals omputer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 led keyboards, 12 of which have electrical defects and 13 of which have mechanical defects. DevoreStat9 2.E.034.[13885760] How many ways are there to randomly select 7 of these keyboards for a thorough inspection (without regard to order)? ways n how many ways can a sample of 7 keyboards be selected so that exactly two have an electrical defect? ways sample of 7 keyboards is randomly selected, what is the probability that at least 6 of these will have a mechanical t? (Round your answer to four decimal places.)

Explanation / Answer

Solution:

a) Let A1, A2, A3 denote the day, swing, and night shifts. Let C1, C2 denote unsafe conditions, and unrelated to conditions. The simple events are then all combinations of one A term and one C term.
Simple Events: {(A1, C1), (A1, C2), (A2, C1), (A2, C2), (A3, C1), (A3, C2)}
Therefore, the simple events are as listed above.

b) To determine the probability an accident was attributed to unsafe conditions, add together the probabilities of unsafe conditions for each shift.
P(C1) = P(A1, C1) + P(A2, C1) +P(A3, C1)
= (0.12)+ (0.07) + (0.04)
= 0.23
Thus, the probability an accident was attributed to unsafe conditions is P(C1) = 0.23

c) To determine the probability that an accident did not occur on the day shift, add together all probabilities terms that did not occur during the day shift.
P(A1') = P(A2, C1) +P(A2, C2) +P(A3, C1) +P(A3, C2)
= (0.07) +(0.15) +( 0.04) + (0.33)
= 0.59
Thus, the probability that an accident did not occur on the dat shifts P(A1') = 0.59

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