Surge Protectors Refer to the accompanying figure showing surg...

Question

Surge Protectors Refer to the accompanying figure showing surge protectors p and q used to protect an expensive television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.985 probability of working correctly when a voltage surge occurs.

a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? (Do not round the answer.)

a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? (Do not round the answer.)

Accepted Answer

Welcome back everyone to another video. A network system uses two firewalls, X and Y, to prevent unauthorized access. Each firewall has a 0.97 probability of successfully intercepting an unauthorized attempt. What is the probability that an unauthorized access attempt will be intercepted if both firewalls work independently? So first of all, let's define an event A. We want to find the probability that an unauthorized access attempt will be intercepted, right? So we're going to say that it represents an event that the access will be intercepted. So we want to identify the probability of a, and what we're going to do in this problem is use the method of complements. The probability of A is equal to 1 minus the probability of a not happening, which means we're taking 1 minus the probability of the complement of A. And then we want to identify the probability of a bar, right, the complement of a. Essentially We want to find the probability that both firewalls. Fail and we know that the success rate P is 0.97. So now what is the failure rate? Well, the failure rate for one firewall is P bar, which is 1 minus P. Once again we're using compliments, and that's 1 minus 0.97. So now P of a bar is essentially 1 minus 0.97. Right? Essentially, we're taking the failure rate, and we have to square it because we have two firewalls. Now here we're using the multiplication rule for independent events, right? And now what we have to do is basically substitute it back into the original formula so we can say that the probability of a, the probability of The axis being intercepted is equal to 1 minus 1 minus 0.97 squad, which gives us 0.9991, and that will be our final answer to this problem. Thank you for watching.

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Key Concepts

Probability of Independent Events

Series Configuration

Complementary Probability

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