5.41 Answering homework questions Each question of an online homework consists of two parts. The probability that you answer the first part of a given question correctly is 0.75. Given that you answered the first part correctly, the probability you answer the second part correctly is 0.60.

Given that your missed the first part, the probability that you answer the second part correctly is 0.40.

a. What is the probability that you answer both parts of a given question correctly?

b. Find the probability that you answer one of the two parts correctly (i) using the multiplicative rule with the two possible ways you can do this and (ii) by defining this as the complement of answering correctly neither or both of the two parts.

c. Are the results of the two parts independent? Explain.