a product designer must decide if a redundant component is cost-justified in a product. the product in question has a critical component with a probability of 0.98 of operating. product failure would involve a cost of $20,000. for a cost of $100, a switch and backup component could be added that would automatically transfer the control to the backup component in the event of a failure. should the backup component be added if its operating probability is also 0.98?