Answer:
0.00335
Step-by-step explanation:
Probability that one of the components works for x hours before failing is given by
f(x) = 2e⁻²ˣ
We can then find the probability that one of the components works for x = 4 hours before failing
f(x) = 2e⁻⁸ = 0.0006709253
Probability that the system works for 4 hours = probability that at least 1 of the components of the system works for 4 hours =
1 - (Probability that none of the components of the system works for 4 hours)
Probability that one of the components doesn't work for 4 hours = 1 - 0.000670925 = 0.9993290747
Probability that none of the 5 components work for 4 hours = (0.9993290747)⁵ = 0.9966498721
Probability that the system works for 4 hours = probability that at least 1 of the components of the system works for 4 hours
= 1 - (Probability that none of the components of the system works for 4 hours)
= 1 - 0.9966498721 = 0.0033501279
Hope this Helps!!!
