After the function, the chef notes that 27 chose Main A, while the remaining 63 chose Main B. And of the people that chose main A, 15 chose Dessert A and 12 chose Dessert B. Of the people that chose Main B, 14 chose Dessert A and 49 chose Dessert B. a) A tree diagram describing this situation has been drawn up, and some probabilities have been filled in. Complete the tree diagram for this scenario by filling in the appropriate probability for each part of the tree. Give your answers as decimals to 2 decimal places. Dessert A 0.56 Main A 0.30 Dessert B 0.44 Dessert A 0.22 Main B 0.70 Dessert B 0.78 b) Find the probability that a random person from this group selects Main A and Dessert B. Give your answer as a decimal to 2 decimal places. P(Main A and Dessert B) = 0.13 c) Find the probability that a random person from this group selects Dessert B given that they selected Main A. Give your answer as a decimal to 2 decimal places. P(Dessert B| Main A) = 44 3 of 3 ID: MST.FET.P.CP.03.0040A [2 marks] For the random process of rolling two six-sided dice and recording the sum, let A and B be the events defined by: A: the result is an odd number B: the result is less than or equal to 9 a) Calculate the probability of B given A. Give your answer as a decimal to 2 decimal places. P(BIA) - b) Calculate the probability of A given B. Give your answer as a decimal to 2 decimal places. P(A|B)