(15 marks). Based on the book coding of question 2, the following two way table (also called a cross-tabulation table) was created. The rows contain the classification by subject and the columns contain the classification by colour. The numbers in the table are the frequencies of the combination of subject and colour of the book cover. For example, there were two books whose subject was computers and for which the primary colour of the cover of the book was blue. Blue Green White Yellow B G W Y Totals Computers C 2 1 1 4 8 Math M 1 1 2 9 13 Physics P 4 4 2 3 13 Other O 0 2 3 1 6 Totals 7 8 8 17 40 Let be the event "colour is Blue". Let be the event "colour is Green". Let be the event "colour is White". Let be the event "colour is Yellow". Let be the event "topic is Computers". Let be the event "topic is Math". Let be the event "topic is Physics". Let be the event "topic is Other". NOTE: to answer the following questions, you may use the table (or create the corresponding probability table), probability formulas or reasoning about sets and probabilities. All probability answers should be expressed to three digits after the decimal point. (4 marks). Find the following marginal probabilities: , , and (5 marks). Find and and or Express your answer for and in words in a complete sentence. (2 marks). Which pair of events, one from subject and one from colour, are mutually exclusive? Provide a valid reason for your answer (a guess without valid reason is worth zero). (4 marks). Determine if the events and are independent. You must show some valid calculations to demonstrate an explanation for your answer (a guess without a valid reason is worth zero).