Question 5 (Unit 8) - 11 marks Assume that of all individuals buying a certain mobile phone at a phone shop: 60% include extra memory in their purchases; of those buyers who buy the phone with extra memory, 75% also buy the phone with larger capacity battery. (a) Let M denote the event 'buy the phone with extra memory', and let B denote the event 'buy the phone with larger capacity battery'. Write the information given in the two bullet points in symbolic form. [2] (b) Calculate the probability that a randomly chosen buyer buys a phone with both extra memory and larger capacity battery. [2] (c) Additional information is now given that 52% of the buyers in this shop do not buy the mobile phone with a larger capacity battery. Calculate the probability that a randomly chosen buyer in this phone shop who buys the phone with larger capacity battery also buys the phone with extra memory. [3] (d) What percentage of buyers in this shop buy either the phone with extra memory or with larger capacity battery (or both)? [2] (e) For the buyers in this shop, are the events of buying the phone with extra memory and buying the phone with larger capacity battery independent? Justify your answer. [2]