SOLUTION: Hello, Any help is much appreciated, having a hard time wrapping my head around probability. Question: Armco, a manufacturer of traffic light systems found that under accelerat

Algebra ->  Probability-and-statistics -> SOLUTION: Hello, Any help is much appreciated, having a hard time wrapping my head around probability. Question: Armco, a manufacturer of traffic light systems found that under accelerat      Log On


   

Question 425915: Hello,
Any help is much appreciated, having a hard time wrapping my head around probability.
Question:
Armco, a manufacturer of traffic light systems found that under accelerated life tests 95% of the newly developed systems lasted 3 years before failing to change signals properly.
a)If a city purchases 4 of these systems, what is the probability that all 4 systems would operate properly for at least 3 years?
b)Which rule of probability does this illustrate?
c)using letters to represent the four systems, write an equation to show how you arrived to the answer to part a.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
probability of 1 system lasting 3 years before failing is .95

probability of all 4 systems lasting 3 years is .95*.95*.95*.95 = .81450625.

the formula that applies is p(a intersect b) otherwise known as p(a and b)

p(a intersect b) or p(a and b) equals p(a) * p(b)