Video Transcript
A CD company uses the following procedure to check if the CD is acceptable for data storage. Data must read back immediately after being written. If the readback fails three times, then that CD is eliminated as unacceptable. The probability of a successful readback on a CD is 0.98. Assuming that the readbacks are independent, find the probability that an acceptable portion will not be eliminated.
We are told in the question that the probability of a successful readback on a CD is 0.98. As probabilities sum to one and there are two possible outcomes, success and failure, then the probability of failure is equal to one minus 0.98. This is equal to 0.02. We know that for any two independent events, the probability of 𝐴 and 𝐵 is equal to the probability of 𝐴 multiplied by the probability of 𝐵. As the readbacks are independent, we can use this in this question.
We are told that the CD is eliminated if the redback fails three times. This means that it is equal to 0.02 multiplied by 0.02 multiplied by 0.02. This can be rewritten as 0.02 cubed, which in turn is equal to 0.000008.
We are asked to calculate the probability that the CD is not eliminated. This is the complement of our previous answer. And the probability of the complement plus the probability of the event itself must sum to one. One minus 0.000008 is equal to 0.999992. This is the probability that an acceptable portion will not be eliminated.
