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Post your solutions to all the questions. You are required to show all relevant steps. Be reminded to respond to at least one posts made by your peers. Your response must be constructive, that is, it must add new insight and foster further interaction. Question 1 a) Two events, A and B. are such that PM U B) = 0.86. HR) = 0.72 and PM) = 0.64. Determine (i) P (A n E) (ii) P (All?) (iii) P (A U B)' b) For a group of 300 cars the numbers. classied by colour and country of manufacture. are shown in the table. Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is (i) a black or white car manufactured in Korea. ' (ii) not manufactured in Japan. (iii) is a white cat. given that it was manufactured in America. (iv) Are the events 'Korea' and 'Black' Mutually Exciusive? Justify your response. (v) Are the events 'Korea' and 'Black' Independent? Justify your response Question 2 a) There is small parking lot behind a Floral Shop that has two parking lot spaces. Let X be the number of cars parked in the parking lot at midday. The probability distribution of X is given by x P(X=x) =T x=o,1,2 (i) Construct the probability distribution table (ii) What is the probability that there will be at most 1 car in the parking lot? (iii) Calculate the expected number of cars in the parking lot at midday Question 3 _. a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet (i) Define the random variable for this situation and list its values (ii) Stating its parameter\"), what is the probability distribution of this variable? (iii) State the conditions that inuence your choice of distribution. (iv) Calculate the probability that at most 2 of the roses were Eden Roses. b) The number of telephone calls coming into Grace Floral Shop to place orders averages 3 per minute. (i) Define the random variable in this situation and list its values. (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii) Compute the probability that 5 calls will arrive per minute. (iv) Compute the probability that 3 or more calls will arrive in a limit-lute interval? Hut-anion 4 The time taken by employees at Grace Floral shop to put a bouquet together has a normal distribution with mean 26.4 minutes and standard deviation .8 minutes. (i) Find the probability that an employee chosen at random takes between 24.6 and 27.8 minutes to put a bouquet together. (ii) 12% of employees take more than t minutes to put a bouquet together. (ii) Find the value of t. The review response contributes 5 marks Your response must be constructive, that is, it must add new insight and foster farther interaction
