2. In a Grade 7 class, we find that of all pupils, 15% love Mathematics, 30% love English, 20% love Science, and 25% love both Mathematics and English. a) What is the probability that a pupil loves Mathematics or English? b) What is the probability that a pupil loves Mathematics if they love English? c) Is a pupil loving Mathematics independent of loving English? Give the reason. 3. Suppose we are involved in an experiment of observing the sex of the children in families having three children. a) Construct a tree diagram showing the sample space of the experiment UU-MTH-2000-MW - Statistics Week 2 - Individual Written Task Page 1 b) How many outcomes would we have from the tree diagram constructed in a)? Prove the answer given by the multiplication technique of counting. c) What is the probability that i) At least one of the children is a boy? ii) None of the children are girls? iii) All of the children are boys? iv) All the children are of the same sex? 4. The Bursaries' Committee of a certain country offers scholarships to only 4 students from a particular school who come out first, second, third and fourth in their final year examinations. a) Find the number of ordered ways the students can qualify for a scholarship if the school has 10 students sitting for their final examinations. b) If out of 10 students that sat for the examinations, 6 were girls, find the probability that all 4 qualified students in a) above were girls? 5. Solve for exercise 4. Above where order is not important. UU-MTH-2000-MW - Statistics Week 2