Answer Happy

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(ANB) = 0.5? Why or why not? (Hint: For any two sets A and B if A is a subset of B then P(A) S P(B).] No, this is not possible. Since B is contained in the event An B, it must be the case that P(ANB) = P(B). However 0.5 > 0.3 violates this requirement. No, this is not possible. Since B is equal to An B, it must be the case that P(ANB) = P(B). However 0.5 > 0.3 violates this requirement. Yes, this is possible. Since B is contained in the event ANB, it must be the case that P(B) SPAN B) and 0.5 > 0.3 does not violate this requirement. Yes, this is possible. Since An B is contained in the event B, it must be the case that P(B) SPAN B) and 0.5 > 0.3 does not violate this requirement. No, this is not possible. Since AB is contained in the event B, it must be the case that P( AB) = P(B). However 0.5 > 0.3 violates this requirement. X (b) From now on, suppose that P(ANB) = 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? 0.3 X (d) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard. O An B' O AUB O AUB OA'ов Calculate the probability of this event. (e) Calculate the probability that the selected student has exactly one of the two types of cards.