Q25, chapter 5, intoduction to probability, Blitzstein. Please solve this question:Alice is trying t

Q25, chapter 5, intoduction to probability, Blitzstein. Please solve this question:Alice is trying to transmit to Bob the answer to a yes-no question, using a noisy channel.She encodes “yes” as 1 and “no” as 0 , and sends the appropriate value. However, the channel adds noise; specifically, Bob receives what Alice sends plus a N(0, ?2) noise term (the noise is independent of what Alice sends). If Bob receives a value greater than 1/2 he interprets it as “yes”; otherwise, he interprets it as “no”.(a) Find the probability that Bob understands Alice correctly.(b) What happens to the result from (a) if ? is very small? What about if ? is verylarge? Explain intuitively why the results in these extreme cases make sense.