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An aircraft has three engines $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. The aircraft crashes if all the three engines fail. The probabilities of failure are $0.03,0.02$ and $0.05$ for engines $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ respectively. What is the probability that the aircraft will not crash?
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The correct answer is:
$0.99997$
Since, probabilities of failure for engines A, B and C $\mathrm{P}(\mathrm{A}), \mathrm{P}(\mathrm{B})$ and $\mathrm{P}(\mathrm{C})$ are $0.03,0.02$ and $0.05$ respectively.
The aircraft will crash only when all the three engine fail. So, probability that it crashes $=\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{C})$
$=0.03 \times 0.02 \times 0.05$
$=0.00003$
Hence, the probability that the aircraft will not crash, $=1-0.00003$
$=0.99997$
The aircraft will crash only when all the three engine fail. So, probability that it crashes $=\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{C})$
$=0.03 \times 0.02 \times 0.05$
$=0.00003$
Hence, the probability that the aircraft will not crash, $=1-0.00003$
$=0.99997$
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