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In a fruit‐packing facility, 3% of apples are bruised, and the remaining 97% are unbruised. A quality‐control scanner tests each apple:
Let B= apple is bruised and U= apple is unbruised.
Let T= scanner flags apple as bruised and T′= scanner does not flag.
It is known that P(T∣B)=0.95 and P(T∣U)=0.08.
Calculate P(B∩T).
An apple is flagged.
Determine the probability it is actually bruised, P(B∣T).
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At a logistics hub two events are recorded for every shipment :
E : The shipment arrives at the hub on schedule.
F : The shipment leaves the hub on schedule.
It is given that the chance a shipment arrives on schedule is 60%, the chance a shipment leaves on schedule is 80%, and the chance a shipment both arrives and leaves on schedule is 50%.
Show that events E and F are not independent.
Find P(E∩F′).
Given that a shipment arrives on schedule, find the probability it does not leave on schedule.
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