Question

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?

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%.