The probability of failure during one year of operation for a specific brand 100

Question

The probability of failure during one year of operation for a specific brand 100 ohm resistor is 0.001 and the probability of failure for a particular transformer is 0.002. When these two components are installed into a power supply, the probability that that power supply will fail (one or both components fails) is 0.0025.

a. What is the probability that both the resistor and transformer will fail in this period?

b. What is the probability of a resistor failure given a transformer failure?

c. Is the failure of the resistor independent of the failure of the transformer?

Explanation / Answer

a) P(one or both fail) = P(resistor fail) + P(transformer fail) - P(both fail)

P(both fail) = 0.001+0.002-0.0025 = 0.0005

b) P(resistor fail | transformer fail) = P(both fail)/P(transformer fail) = 0.0005/0.002 = 0.25

c) No they are dependent as P(resistor fail | transformer fail) is not equal to P(resistor fail)

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