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Unformatted text preview: 1pm ­7am) 66 5% 90% 5% Total 167 You choose the first accident to investigate at random. Find the probability that: a) The accident was caused by unsafe conditions. b) If the accident was caused by unsafe conditions, it occurred on the graveyard shift. Answer: U: unsafe conditions only; H: human error only B: both contributed D: day E: evening G: graveyard P(U|D)=20%, P(H|D)=77%, P(B|D)=3%, P(U|E)=15%, P(H|E)=81%, P(B|E)=4%, P(U|G)=5%, P(H|G)=90%, P(B|G)=5% P(D)=58/167=0.3473 P(E)=43/167=0.2575 P(G)=66/167=0.3952 a) Add up all the accidents caused by unsafe conditions only and both contributed during day, evening and graveyard shifts. P(U)=P(D⋂U)+P(E⋂U)+P(G⋂U) = P(D)*P(U|D)+ P(E)*P(U|E)+P(G)*P(U|G) =0.3473*0.2+0.2575*0.15+0.3952*0.05 =0.1278 P(B)= P(D⋂B)+P(E⋂B)+P(G⋂B) = P(D)*P(B|D)+ P(E)*P(B|E)+P(G)*P(B|G) =0.3473*0.03+0.2575*0.04+0.3952*0.05 =0.0405 P(U⋃...
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