# Math Help - Probability Question (reliability)

1. ## Probability Question (reliability)

Hello,

I am having a hard time figuring this question out. Please help me out as I am struggling on this problem. Thanks!

Here are two unrelated probability questions.
1 Determine the system reliability of the following communication system. There are two different methods of communicating; at least one method must succeed in order for the system to succeed. The first method is by an FM radio, which has reliability 75%. The second method is by a satellite radio; both the physical radio must transmit the signal (with 90% reliability) AND the satellite must retransmit the signal (with 95% reliability) in order for the satellite radio to succeed.

2 Suppose that you are modeling the arrival of patients at a doctor's office in the first five minutes, starting at 9am. Suppose that at every minute (9:00, 9:01, 9:02, 9:03, 9:04), there is a probability of 0.075 that a patient arrives. What is the probability that the first patient arrives at 9:01? the first patient arrives at 9:02? the first patient arrives at 9:03? the first patient arrives at 9:04? What is the probability that no patients arrive in these first five minutes?

2. Originally Posted by Martin Billado
Hello,

I am having a hard time figuring this question out. Please help me out as I am struggling on this problem. Thanks!

Here are two unrelated probability questions.
1 Determine the system reliability of the following communication system. There are two different methods of communicating; at least one method must succeed in order for the system to succeed. The first method is by an FM radio, which has reliability 75%. The second method is by a satellite radio; both the physical radio must transmit the signal (with 90% reliability) AND the satellite must retransmit the signal (with 95% reliability) in order for the satellite radio to succeed.
The reliability of the satellite radio is $r_{sat}=0.9 \times 0.95 = 0.855$ or $85.5\%$ (sub-systems in series)

The reliability of the system is $r= 1-(1-r_{fm})(1-r_{sat})\approx 0.964$ or $96.4 \%$ (sub-systems in parallel)

CB

3. Originally Posted by Martin Billado

2 Suppose that you are modeling the arrival of patients at a doctor's office in the first five minutes, starting at 9am. Suppose that at every minute (9:00, 9:01, 9:02, 9:03, 9:04), there is a probability of 0.075 that a patient arrives. What is the probability that the first patient arrives at 9:01? the first patient arrives at 9:02? the first patient arrives at 9:03? the first patient arrives at 9:04? What is the probability that no patients arrive in these first five minutes?
For the first patient to arrive at 9:01 means that no patient arrived at 9:00 and one arrived at 9:01. So now you can calculate this probability.

If you are still having trouble tell us exactly what the problem is and tell us what you have done.

CB