Aspace vehicle has an independent backup system for one of its communication networks. the probability that either system will function satisfactorily during a flight is 0.985. what is the probability that during a given flight (a) both systems function satisfactorily, (b) at least one system functions satisfactorily, and (c) both systems fail?

(a) P (Both systems functioning satisfactorily) = 0.970

(b) P (At least one system functions satisfactorily) = 0.999

(c) P (Both the systems failing) = 0.00023

Step-by-step explanation:

Let A = the system in use is working satisfactorily and B = the backup system is working satisfactorily.

The probability that either of the systems works satisfactorily is,

P (A) = P(B) = 0.985

(a)

Both the events A and B are independent, i.e.

Compute the probability that during a given flight both systems function satisfactorily as follows:

Thus, the probability of both systems functioning satisfactorily is 0.970.

(b)

Compute the probability that during a given flight at least one system functions satisfactorily as follows:

P (At least one system functions satisfactorily) = 1 - P (None of the system functions satisfactorily)

                                                                             =

Thus, the probability that during a given flight at least one system functions satisfactorily is 0.999.

(c)

Compute the probability that during a given flight both the systems fail as follows:

P (Both the systems failing) =

Thus, the probability that during a given flight both the systems fail is 0.00023.