(a) Define the following terms as used in probability. (i) Independent events. (ii) Conditional probability. (iii) Outcome. (iv) Event. [4 Marks] (b) Ninety students will graduate from Alpha High School this year. Out of the 90 graduates, 50 are planning to attend college. Two students are selected at random to carry the flag at graduation. What is the probability that both of them are planning to attend college? [4 Marks] (c) The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina, for the last 50 days. To explain, there were 22 days on which there were two emergency calls, and 9 days on which there were three emergency calls. Number of calls 0 1 2 3 4 Frequency 8 10 22 9 1 (i) Convert this information on the number of calls to a probability distribution. [2 Marks] (ii) What is the mean number of emergency calls per day? [2 Marks] (iii)What is the standard deviation of the number of calls made daily? [2 Marks] (iv) ) A and B are two events such that 1(/)4PAB and 1(/)5PBA.Given that ()PABp find (i) ()PA (ii) ()PB [2 Marks] (v) (iii) Suppose 1()5PAB find the value of p [4 Marks]