(20 pts) Basic Probability (a) (4 pts) Which of the following expressions is guaranteed to be 1, given two random variables X and Y, and no independence or conditional independence assumptions between them are given? For each expression, show why and why not it is guaranteed to be 1 . -y∑ P(X=x∣Y=y)-x∑ P(X=x∣Y=y)x∑y∑ P(X=x∣Y=y)-x∑P(X=x)+ y∑P(Y=y)(b) (4 pts) Given two Boolean random variables A and B , where P(A)= 21 ,P(B)= 4 1, andP(A∣¬B)= 31, apply Bayes's rule and calculate the value ofP(A∣B)