Question

A satellite system consists of 4 components and can function if at least 2of them are working. If each component independently works with probability 0.8, what is the probability the system will function?

Answer 1

0.9728

Explanation:

We have 2 options for the system to fail - no components work, or only one works.

The probability that no components work is:

`0.2^4 = 0.0016`

The probability that one SPECIFIC component works and the others failed is:

`0.2^3 \cdot 0.8 = 0.0064`

And because there's 4 components, the chance that EXACTLY ONE works but the others don't is:

`4 \cdot 0.0064 = 0.0256`

So we sum the probabilities:

`P_(failure) = 0.0016 + 0.0256 = 0.0272\\P_(works) = 1 - P_(failure) = 0.9728`

Answer 2

X follows binomial distribution with n=4, p=0.6, q= 0.4. To make the system function adequately, at least 2 components should work well.

Explanation:

Hope this helps