1 of 3 ID: MST.FET.P.CP.01.0010A [7 marks] A survey is conducted at a university involving 1,500 students. The students are either male or female and are also either domestic students or international students. The results of the survey show that 786 students are female and 538 students are international students. Further, 382 are female international students; 404 are female domestic students; 156 are male international students; and 558 are male domestic students. Let the events A and B be: Event A: a random student is female Event B: a random student is an international student a) An incomplete tree diagram for this scenario is presented below. Fill in the appropriate probability for each part of the tree. Give your answers as decimals to 2 decimal places. International Female Domestic International Male Domestic b) Find the probability that a random student from this group is an international student given that they are female. Give your answer as a decimal to 2 decimal places. P(B given A) = 2 of 3 ID: MST.FET.P.CP.02.0020A [6 marks] A large group of 90 people sit down at a function to a two-course meal. Each course has two options: guests can choose to have either Main A or Main B, and they can choose to have either Dessert A or Dessert B. 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 0.17- Main A 0.30