Single error correction-double-error detection (SEC-DED) codes are often employed in systems with error- correcting code (ECC) memory. SEC-DED codes can correct if there is a single bit in a memory word that is flipped, and can detect (but not correct) if two bits are flipped. If the size of a memory word is 4 bytes, and the probability of a bit being flipped is 0.2, then answer the following questions.

1. a) What is the probability that all bits in a memory word are correctly set (without any SEC-DED corrections)?

2. b) What is the probability that SEC-DED can detect an error but not correct it?

3. c) What is the probability that there are exactly two bits incorrectly flipped in a memory word, if we already know that one bit is flipped incorrectly?

4. d) If the content of a memory is known to be correct, what is the probability that it was corrected by SEC-DED?