Mathematics: Acommunications circuit is known to have an availability of 0.99 (that is, 99% of the time, the circuit is operational). a total of n such circuits are going to be set up by the faa between san francisco and los angeles in such a way that the circuits will fail indepen- dently of each other. how many such parallel circuits must be set up to attain an overall availabililty of 0.

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Acommunications circuit is known to have an availability

Ответ:

tinapersaud1587

16.01.2022

Assume that for the communication to be available means that at least one of the circuits is operational. It would take at least 3 circuits to achieve a 0.99999 overall availability.

Step-by-step explanation:

The probability that one circuit is not working is 1 - 0.99 = 0.01 .

Since the circuits here are all independent of each other, the probability that none of them is working would be $\displaystyle \underbrace{0.01 \times 0.01 \times \cdots \times 0.01}_{\text{$n$ times}}$ . That's the same as 0.01^n .

The event that at least one of the circuits is working is the complement of the event that none of them is working. To find the probability that at least one of the circuits is working, simply subtract the probability that none of the circuit is working from one. That is:

$\begin{aligned}&P(\text{At least one working}) \cr &= 1 - P(\text{None is working}) \cr &= 1- 0.01^n\end{aligned}$ .