What Is the Probability of a Computer Being Operational for 100 Days?

[estado3]

Homework Statement

Assuming a comp is switche don, the probability that the monitor is not working is 0.005, the probability that the CPU is faulty is 0.02, and the probability that the keyboard cable has been damaged is 0.0025, and that there are no other faults.

Proceed to evaluate the probability that the computer will be operaitonal for a period of 100 days, if it is switched on and off once a day only, and that the faults have the same probability of occurrence on each occasion

Homework Equations

The Attempt at a Solution

I tried to find the probability that the comp will be operational i.e
p(monitorfailing) +p(cpufaulty) + p(cable damaged) = p(systemfailure)

0.005 + 0.002 + 0.0025 = 0.0095

My next assumption is the value above is the probability of the comp working for one day, and to simply multiply by 100 i.e 0.95 to get the probability of the comp working for 100 days, however I am way off and the answer is 0.386058

 

[real10]

Homework Statement

Assuming a comp is switche don, the probability that the monitor is not working is 0.005, the probability that the CPU is faulty is 0.02, and the probability that the keyboard cable has been damaged is 0.0025, and that there are no other faults.

Proceed to evaluate the probability that the computer will be operaitonal for a period of 100 days, if it is switched on and off once a day only, and that the faults have the same probability of occurrence on each occasion

Homework Equations

The Attempt at a Solution

I tried to find the probability that the comp will be operational i.e
p(monitorfailing) +p(cpufaulty) + p(cable damaged) = p(systemfailure)

0.005 + 0.002 + 0.0025 = 0.0095

My next assumption is the value above is the probability of the comp working for one day, and to simply multiply by 100 i.e 0.95 to get the probability of the comp working for 100 days, however I am way off and the answer is 0.386058

u started right with adding them up to get system failureP (Failure)=0.0095
but the question asks when it will be operational! so P(operational)= 1-P(failure)
then 100 days would [P(operational) ] ^100. because each day has the same probability of success so u multiply it by itself 100 times.

 

[estado3]

The question then says that the conditional probability of the monitor not working given that the keyboard cable has been damaged is 0.05, and askes how it affects the answers

the solution is 0.390459

but I am thinking that
the probability of failure of the monitor is now
0.005 X 0.05

overall 1 - probability of failure of the system is now
(1 - (0.005 X 0.05 + 0.002 + 0.0025) ) ^100