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Guessing the Value of p

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A production line manager, J, is trying to design a manufacturing line, using the machines that her company already has. Based on the historical records, each individual candidate machine will fail, during the production, with a probability of 1-p, and their failures are independent. Since the company plans to discard the machines after the production, J has no budget to repair any failure machine. The line is considered as working properly if at least 50% of the machine(s) in the line remain operative, otherwise the production is considered failed. There are two options for line design:

a. Using four machines.
b. Using two machines.

And J, based on the value p, selected option b. Please guess the value of p.

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The solution determines the value of p for a production line.

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