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?

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apokibunnyavatar apokibunnyavatar · Answer 1 · 2021-04-09T12:50:05+02:00

Answer:

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.

Step-by-step explanation:

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janmilczek janmilczek · Answer 2 · 2021-04-09T12:52:48+02:00

Answer:

0.9728

Step-by-step explanation:

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

The probability that no components work is:

[tex]0.2^4 = 0.0016[/tex]

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

[tex]0.2^3 \cdot 0.8 = 0.0064[/tex]

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

[tex]4 \cdot 0.0064 = 0.0256[/tex]

So we sum the probabilities:

[tex]P_{failure} = 0.0016 + 0.0256 = 0.0272\\P_{works} = 1 - P_{failure} = 0.9728[/tex]