6. Your experiment is throwing two 6-sided dice and recording the outcome as a pair (į, j), where i is the result of the first die and j of the second die. Let A be the event that is 3, let B be the...

M-6 Please I need help with this question needed a very clear and step-by-step explanation and needed with clear handwriting please, will be really appreciated your help.

Extracted text: 6. Your experiment is throwing two 6-sided dice and recording the outcome as a pair (į, j), where i is the result of the first die and j of the second die. Let A be the event that is 3, let B be the event that 3sis 5, and let C be the event that i+j = 9. (a) Calculate the probabilities of each of the events A, B, and C. (b) Calculate the probability of ANBNC and compare with P(A)P(B)P(C). (c) Calculate the probabilities of all pairwise intersection and compare with the products of the probabilities. Are the events A, B, and C mutually independent? (d) It turns out that three events are mutually independent if and only if the three-way equation like in item (b) holds not just for the events themselves, but also any combination of the events and their complements. Since A, B, and C are not mutually independent, there is a combination of A or AC, and B or BC, and C or CC for which the equation from item (b) fails. Find this combination.