A space shuttle is assigned to visit a TV satellite in a GSO (geosynchro-nous orbit) with radius 36,000 km (event A ₁ ), and carry out maintenance (event B ₁ ). Alternatively, it may, due to failure of one of the engines, go into an LEO (low Earth orbit) with radius 200 km (event A ₂ ) and carry out a crop survey (event B ₂ ). B ₁ and B ₂ are regarded as successful performance. The third possibility is failure to take off (event A ₃ ). What is the reliability (probability of successful performance) of the space shuttle if P(B ₁ |A ₁ ) = 0.75, P(B ₂ |A ₂ ) = 0.85, P(A ₁ ) = 0.80, and P(A ₂ ) = 0.15?

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Event B 1 can only o... View the full answer