A space vehicle has an independent backup system for one of its communication networks. The probability that either system will function satisfactorily for the duration of 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 c) both systems fail?

a) 0.970225

b) 0.999775

c) 0.000225

Step-by-step explanation:

probability of one system not working = 1-0.985=0.015

a)

probability of one system is 0.985 then

Probability of both system = 0.985 * 0.985 = 0.970225

b)

probability of one of system fail is = 1 - 0.985

=0.015

Therefore

probability of both system failing = 0.015 * 0.015 = 0.000225

probability at least one system function satisfactorily = 1 - 0.000225

= 0.999775

c)

If both system are fail then probability is 0.000225