Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive vehicles pass or fail independently of one another, calculate the following probabilities:
a) P (all of the three vehicles inspected pass)
b) P (at least one of the next three inspected fails)
c) P (exactly one of the next three inspected passes)
d) P (at most one of the next three vehicles inspected passes)
e) Given that at least one of the next three vehicles passes inspection, what is the probably that all three pass (a conditional probability)?
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Provides steps necessary to determine probability.