Question

Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and 8 be the analogous event for MasterCard. Suppose that P(A)-0.6 and P(B)-0.4 (a) Could it be the case that PLA n B)-0.5 ? why or why not? [Hint: For any two sets A and B d'A is a subset of B then AAS pu).] No, this is not possible. Since A ก B is contained in the evet B, it must be the case that P(A n B) S PrB). However 0.5 > 0.4 violates this requirement. Yes, this is possible. Since B is contained in the event A n B, it must be the case that P(B) s PA n B) and 0.5 > 0.4 does not violate this requirement e Yes, this is possible. Since A η В is contained in the event 8, t must be the case that PO) s PA n B) and 0.5 > 0.4 does not violate this requirement @ No, this is not possible. Since B is equal to A ก B, it must be the case that prA ก B)-PfB). However O .5> 0.4 violates this requirement ained in the event a n B, it must be the case that PA n B) s P(B). However 0.5 04 vWolates this requirement. No, this is not possible. Since is contained in the event A n B, it must be the c (b) From now on, suppose that prA ก 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. @ А.UB AUB Calculate the probability of this event. Activate Windows Go to Settings to activate (e) Calculate the probability that the selected student has exactly one of the two types of cards

Answer 1