A satellite system consists of 4 components and the system can function if at
least 2 components are working. If each component independently works with probability
0.8, what is the probability the system will function?
Can anyone help?
[Math] Simple-ish probability question
probability
Best Answer
The system will not work, if 3 or 4 components are not working. We can calculate the probability for that:
$P($all components are broken$) = 0.2^4 = 0.0016$
$P($3 components are broken$) = {4 \choose 3} \cdot 0.2^3 \cdot 0.8^1 = 0.0256$
So the chance that the system is not running is $0.0016 + 0.0256 = 0.0272$. Therefore the chance that the system is running is $1-0.0272 = 0.9728$.