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

Robert Peck

Mathematics

11 January, 17:38

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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Jj · 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%.