Spare power supply units for a communications terminal are provided to the gover

Question

Spare power supply units for a communications terminal are provided to the government from three different suppliers A_1, A_2, and A_3. Thirty percent come from A_1, 20% come from A_2, and 50% come from A_3. Suppose these units occasionally fail to perform according to their specifications and the following has been observed: 2% of those supplied by A_1 fail, 5% of those supplied by A_2 fail, and 3% of those supplied by A_3 fail. What is the probability any one of these units provided to the government will perform without failure?

Explanation / Answer

P(no failure)=1-P(failure)

P(failure)=0.3*0.02+0.2*0.05+0.5*0.03=0.031

P(no failure)=1-0.031 = 0.969

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