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Consider randomly selecting a student at a large university and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard Suppose that P A 0 7 and P B 0 3 a Could it be the case that P A n B 0 5 Why or why not Hint For any two sets A and B if A is a subset of B then P A P B Yes this is possible Since B is contained in the event A n B it must be the case that P B P An B and 0 5 0 3 does not violate this requirement Yes this is possible Since A n B is contained in the event B it must be the case that P B P An B and 0 5 0 3 does not violate this requirement No this is not possible Since B is equal to An B it must be the case that P A n B P B However 0 5 0 3 violates this requirement No this is not possible Since A n B is contained in the event B it must be the case that P A n B P B However 0 5 0 3 violates this requirement No this is not possible Since B is contained in the event A n B it must be the case that P A n B P B However 0 5 0 3 violates this requirement b From now on suppose that P An B 0 2 What is the probability that the selected student has at least one of these two types of cards c What is the probability that the selected student has neither type of card d Describe in terms of A and B the event that the selected student has a Visa card but not a MasterCard AUB An B OA U B A n B Calculate the probability of this event P J B e Calculate the probability that the selected student has exactly one of the two types of cards S E O 20

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