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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 PM) : 0.7 and P(B) : 0.4. (a) Could it be the case that P(A f'l B) : 0.5? Why or why not? [Hint For any two sets A and B ifA is a subset of B then P(A) s P(B).] 0 Yes, this is possible. Since A H Bis contained in the event 8, it must be the case that P65) 5 PM Fl B) and 0.5 > 0.4 does not violate this requirement. 0 No, this is not possible. Since Bis contained in the event A n B, it must be the case that P(A n B) S P(B). However 0.5 > 0.4 violates this requirement. 0 No, this is not possible. Since Bis equal to A n B, it must be the case that P(A H B) = P(B). However 0.5 > 0.4 violates this requirement. 0 Yes, this is possible. Since Bis contained in the eventA n B, it must be the case that P(B) s PM n B) and 0.5 > 0.4 does not violate this requirement. 0 No, this is not possible. Since A n Bis contained in the event 5, it must be the case that PM n B) S P(B). However 0.5 > 0.4 violates this requirement. (b) From now on, suppose that PM {'1 B) : 0.3. What is the probability that the selected student has at least one of these two types of cards? :I (c) What is the probability that the selected student has neither type of card? :I (d) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard. 0 A n B' O A' n B O A u B' O A' o B Calculate the probability of this event. :I (e) Calculate the probability that the selected student has exactly one of the two types of cards. :I