A device tests whether each light on a string of LED lights is functioning properly. A company estimates that 2.3% of LED lights that they produce are defective. The device is 96% accurate for lights that are functioning properly and 94% accurate for lights that are defective. You use the device to test a randomly selected light. What is the probability that the test result is correct? Round your answer to the nearest tenth.

Question

Mathematics

Simeon Bradshaw

28 April, 15:49

A device tests whether each light on a string of LED lights is functioning properly. A company estimates that 2.3% of LED lights that they produce are defective. The device is 96% accurate for lights that are functioning properly and 94% accurate for lights that are defective. You use the device to test a randomly selected light. What is the probability that the test result is correct? Round your answer to the nearest tenth.

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Answers (1)

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Frank Mays · Answer 1

96% probability that the test result is correct

Step-by-step explanation:

We have these following probabilities:

2.3% probability that a randomly selected light is defective.

If the light is defective, 94% probability that the test result is correct.

100-2.3 = 97.7% probability that a randomly selected light is not defective.

If the light is not defective, 96% probability that the test result is correct.

What is the probability that the test result is correct?

94% of 2.3% and 96% of 97.7%. So

p = 0.94*0.023 + 0.96*0.977 = 0.96

96% probability that the test result is correct