1. An amateur weather forecaster describes each day as either sunny, cloudy or wet. He keeps a record each day of his forecast and of the actual weather. His results for one particular year are given in the table. A day is selected at random from that year. (i) Show that the probability that the forecast is correct is ggg. [1] Find the probability that (ii) the forecast is correct, given that the forecast is sunny, [2] (iii) the forecast is correct, given that the weather is wet, [2] (iv) the weather is cloudy, given that the forecast is correct. [2] 2. Isobel plays football for a local team. Sometimes her parents attend matches to watch her play. A is the event that Isobel's parents watch a match B is the event that Isobel scores in a match You are given that P(BIA) = % and P(A) = %. (i) Calculate P(A n B). [2] The probability that Isobel does not score and her parents do not attend is 0.1. (ii) Draw a Venn diagram showing the events A and B, and mark in the probability corresponding to each of the regions of your diagram. [2] (iii) Are events A and B independent? Give a reason for your answer. [2]