## Independence

Hi everybody,
I have the following problem that I can't solve...

Let us consider a hard drive with a rate of failure of p = 0.01, thus each bit that is saved on this hard drive is going to get switched independently of all the others with a probability of 1%. To increase reliability, a checksum is stored on the hard drive as well. For 8 bytes of data a single byte is stored as checksum (so there is a total of 9 bytes). The algorithm used for this has the following weakness: If 8 bits of the original data and one bit of the checksum are switched, the result will be false positive, thus the data seem to be ok, although they are not. Analogously, if only bits in the checksum are switched, one retrieves a false negative, i.e., even though the data seem broken, they are not. Given an 8 byte file. What are the probabilities of
a) Reading non-corrupted data and the right checksum (“right-positive”)?
b) Reading corrupted data and an non-fitting checksum (“right-negative”)?
c) Reading corrupted data and a fitting checksum (“false-positive”)?
d) Reading non-corrupted data but an non-fitting checksum (“false-negative”)?

Could someone help me out?
Thanks very much!