Engineers working for an aerospace company are designing coatings for the heat s

Question

Engineers working for an aerospace company are designing coatings for the heat shielding tiles used to line the cone of a rocket. The tiles themselves are heat resistant, but they must be replaced after each launch. To prolong their lifespan, the engineers are applying two different heat resistant coatings. If the coatings work, the tiles can be reused after each launch. There is only a 0.15 probability that the outer most coating fails, and a 0.026 probability that the second layer will fail. Only if both of the coatings fail will the tiles need to be replaced. If both of these coatings are used, what is the probability that the tiles can be reused after a launch

Explanation / Answer

P(Tile can be reused after a launch)

= P(At least one of the coatings work)

= 1 - P(No coating works)

= 1 - 0.15*0.026

= 0.9961

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