Digital data are transmitted as a sequence of signals that represent 0s or 1s. Suppose that such data are being transmitted to a satellite and then relayed to a distant site. Suppose that due to electrical interference in the atmosphere, there is a 1-in-1000 chance that the transmitted 0 will be reversed between the sender and the satellite (i.e. distorted to the extent that the satellites receiver interprets the 0 as a 1) and a 2-in-1000 chance that a transmitted 1 will be reversed.

Suppose that 40% of the transmitted digits are 0s.

1. What is the probability that a transmitted digit is correctly received by the satellite?

2. Assuming independence, what is the probability that all the digits are received correctly (i) if 1000 digits are transmitted (ii) if 10,000 digits are transmitted.

3. Suppose that between the satellite and the receiver, the chances of reversal are twice as large as they were between the sender and the satellite. Assuming independence, what is the probability that a digit reaches the receiver as originally sent?