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A lamp is taken at random from a production line and tested. If the bulb does not light up then either the bulb is faulty

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A lamp is taken at random from a production line and tested. If the bulb does not light up then either the bulb is faulty with a probability of 0.1 or the switch is faulty with a probability of 0.3. Switch and bulb faults are independent of each other. What is the probability that a defective lamp has a switch fault but does not have a bulb fault

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