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.

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 overall availability.

Step-by-step explanation:

The probability that one circuit is not working is .

Since the circuits here are all independent of each other, the probability that none of them is working would be . That's the same as .

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:

.

The question requests that

.

In other words,

.

.

Note that . Hence, the inequality becomes

.

Take the natural log of both sides of the equation:

.

.

, hence . Divide both sides by :

.

.

In other words, at least three parallel circuits must be set up to achieve that availability.

47

step-by-step explanation:

r = 78539458390583095803458309458039485093485 or just 3

step-by-step explanation: