One design for a system requires the installation of two identical components. The system will work if at least one of the components works. An alternative design requires four of these components, and the system will work if at least two of the four components work. If the probability that a component works is 0.9, and if the components function independently, which design has the greater probability of functioning?
What will be an ideal response?
Let X be the number of components of the two in the first design that work. Let Y be the number of components of the four in the second design that work. Then X~ Bin(2,0.9) and Y~ Bin(4,0.9). The probability that the design with two components works is
The probability that the design with four components works is
The design with four components has the greater probability of functioning
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