A and B will take the same 10-question examination. Each question will be answered correctly by A with probability .7, independently of her results on other questions. Each question will be answered correctly by B with probability .4, independently both of her results on the other questions and on the performance of A.

a. Find the expected number of questions that are answered correctly by both A and B.

b. Find the variance of the number of questions that are answered correctly by either A or B.