Question: A satellite system consists of n components and functions on any given day if at least k of the n components function on that day.

A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day each of the components independently functions with probability p1, whereas on a dry day they each independently function with probability p2. If the probability of rain tomorrow is α, what is the probability that the satellite system will function?

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