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The National Aeronautics and Space Administration (NASA) purchased a new solar-powered battery guaranteed to have a failure rate of only 1 in 20. A new system to be used in a space vehicle operates on one of these batteries. To increase the reliability of the system, NASA installed three batteries, each designed to operate if the other batteries in the chain fail. If the system is operated in a practical situation, what is the probability that all three batteries would fail

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Answer:

The probability that all three batteries would fail is given as:

= 0.000125

Step-by-step explanation:

Given that the probability of the new battery failing = 1/20 or 0.05,

Therefore, the probability that all three batteries would fail is given as:

= Probability of battery A failing * Probability of battery B failing * Probability of battery C failing

= P(A)*P(B)*P(C)

= 0.05 * 0.05 * 0.05

= 0.000125

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