1. Tree Diagrams Example Of the total daily output of a specific type of article at a factory, 40% are produced on machine A, 10% on machine B, and 50% on machine C. Of the articles produced on machine A, 60% are red and 40% are green. Of the articles produced on machine B, 30% are red and 70% are green. Of the articles produced on machine C, 50% are red and 50% are green. a)Calculate the probability that an article chosen at random from a day’s total output will be green. b)Given that the chosen article was green, calculate the conditional probability that it was produced on machine A. It is possible to use tree diagrams to solve various probability problems. Using the following example, we see that it is possible to solve it by constructing a tree diagram as well as using the method for total probability.

2. A B G C C G C G C 0.4 0.1 0.6 0.4 0.5 0.3 0.7 0.5 P(G) = (0.4 x 0.4) + (0.7 x 0.1) + (0.5 x 0.5) P(G) = 0.48 a)

3. A B G C C G C G C 0.4 0.1 0.6 0.4 0.5 0.3 0.7 0.5 b) P(A|G) = = 0.4 x 0.4 0.48 = 1 3

4. Exercise 3.6 (Questions 2, 5, 6, 7 and 9) Exercise 3.7 Mathematics Statistics Unit S1 - WJEC