Question

(a) Let (a, b, c) denote the result of throwing three dice of colours, amber, blue and crimson, respectively., e.g., (1, 5, 3) represents throwing amber dice =1, blue dice = 5, crimson dice = 3. What is the probability of throwing these three dice such that the (a, b, c) satisfy the equation b 2 − 4ac ≥ 0? [7 marks]

(b) From a survey to assess the attitude of students in their study, 80% of them are highly motivated, 90% are hard working, and only 5% are neither highly motivated nor hard working. i. Calculate the probability that a randomly selected student is both highly motivated and hard working. [3 marks] ii. Given that the student is hard working, what is the probability that this student is not highly motivated?

Answer 1