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Both undergraduates and postgraduates can use the university cafeteria. Each diner can choose between buying a meal or bringing a packed lunch. (Everyone has exactly one meal each, no more and no less). The cafeteria offers a daily choice between a hot meal or a cold meal. A survey of undergraduate diners finds that 40% of them bring their own food. Overall, only 25% of the diners bring their own food. Postgraduates make up one fifth of the diners in the cafeteria.
a) What is the probability that a diner is an undergraduate and has bought a meal?
b) What is the probability that someone who has bought a meal is a postgraduate?
c) Give two different examples from the question of mutually exclusive events.
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