Problem 197SE

An optical storage device uses an error recovery procedure that requires an immediate satisfactory readback of any written data. If the readback is not successful after three writing operations, that sector of the disk is eliminated as unacceptable for data storage. On an acceptable portion of the disk, the probability of a satisfactory readback is 0.98. Assume the readbacks are independent. What is the probability that an acceptable portion of the disk is eliminated as unacceptable for data storage?

Solution

Step 1 of 1

We have to find the probability of the disk is eliminated as a unacceptable for storage

Given that the sector will be eliminated if the read back is not successful for 3 operations

The probability of satisfactory readback is 0.98

Let A be the event that 1st time is not satisfactory readback

Then

=0.02

Let B be the event that 2nd time is not satisfactory readback

Then

=0.02

Let C be the event that 3rd time is not satisfactory readback

Then

=0.02

The three events A, B and C are independent

Then

=

=

=

=

=

=0.000008

Hence the probability of the disk is eliminated as a unacceptable for storage is 0.000008