Doc Brown's DeLorean has three crucial systems that are required for a successful trip: combustion engine, time circuits, and flux capacitor. The combustion engine is necessary to reach a target speed of 88mph and has a reliability of 0.94. To set the destination coordinates, there are four time circuits, each with a 75% chance of working. Luckily, only one working time circuit is needed for a successful trip. The flux capacitor is made of three identical capacitors working together. Each capacitor has a reliability of 0.8. To properly handle the 1.21 Gigawatts and make a successful trip, Doc Brown needs at least two of the three capacitors to function. What is the reliability of the DeLorean making the trip?

Question

Mathematics

Alma

18 January, 18:47

Doc Brown's DeLorean has three crucial systems that are required for a successful trip: combustion engine, time circuits, and flux capacitor. The combustion engine is necessary to reach a target speed of 88mph and has a reliability of 0.94. To set the destination coordinates, there are four time circuits, each with a 75% chance of working. Luckily, only one working time circuit is needed for a successful trip. The flux capacitor is made of three identical capacitors working together. Each capacitor has a reliability of 0.8. To properly handle the 1.21 Gigawatts and make a successful trip, Doc Brown needs at least two of the three capacitors to function. What is the reliability of the DeLorean making the trip?

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Answers (1)

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Camila · Answer 1

Step-by-step explanation:

The total probability that the DeLorean makes the trip is:

P = P (engine) * P (at least 1 time circuit) * P (at least 2 capacitors)

P = P (engine) * (1 - P (0 time circuits)) * P (at least 2 capacitors)

P = 0.94 * (1 - ₄C₀ 0.75⁰ 0.25⁴) * (₃C₂ 0.8² 0.2¹ + ₃C₃ 0.8³ 0.2⁰)

P = 0.94 * (1 - 0.25⁴) * (0.384 + 0.512)

P = 0.83895

The reliability of the DeLorean is approximately 83.9%.