A computer receives input over a slightly faulty connection. For a particular transmission, 80% of the bits sent consists of 0's; the rest are 1's. You can assume that each bit of data is independent of each other bit. The 0's have a 95% chance of being received correctly; the 1's have a 90% chance of being received correctly. Anything which is not received correctly is received as the other number.
a) Overall, what percent of the data is received as a 0?
b) What is the chance that a 0 is received OR a 1 is sent?
c) For a given set of 10 bits, what is the chance that exactly 2 bits sent are 1's?
d) What is the chance that a 1 is sent, given that a 1 is received?