• When data are transmitted over the internet, errors can occur, but they are rare. Let us suppose that when a stream of bits (1's and 0's) are transmitted, each, independently of all the others, has a probability of about one in a million of being read incorrectly.Suppose you email a picture to a friend that is 24.4Kb, or about 200,000 bits. What's the probability that no errors will occur in the transmission?
• Now suppose that this picture gets emailed around 10 times from person to person. What's the probability that after 10 transmissions, there are still no errors from the original picture?
• Make a plot showing on the horizontal axis, number of bits read incorrectly after 10 transmissions, and on the vertical axis, the probability thatat leastthat many bits would be read incorrectly. (Think very carefully about how you will implement the "at least" part.)
• (A comment: corruption in data files is sometimes used to measure how much the files have been passed around. The technique is even used by historians to estimate how many times a text has been copied, counting number of copying errors from the original.)