t be the case that P(An 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).] o, this is not possible. Since An B is contained in the event B, it must be the case that P(AB) ≤ P(B). However 0.5 > 0.3 violates this requirement. es, this is possible. Since An B is contained in the event B, it must be the case that P(B) ≤ P(AB) and 0.5 > 0.3 does not violate this requirement. o, 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. o, 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. es, this is possible. Since B is contained in the event A n B, it must be the case that P(B) ≤ P(ANB) and 0.5 > 0.3 does not violate this requirement. ow 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? the probability that the selected student has neither type of card?
t be the case that P(An 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).] o, this is not possible. Since An B is contained in the event B, it must be the case that P(AB) ≤ P(B). However 0.5 > 0.3 violates this requirement. es, this is possible. Since An B is contained in the event B, it must be the case that P(B) ≤ P(AB) and 0.5 > 0.3 does not violate this requirement. o, 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. o, 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. es, this is possible. Since B is contained in the event A n B, it must be the case that P(B) ≤ P(ANB) and 0.5 > 0.3 does not violate this requirement. ow 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? the probability that the selected student has neither type of card?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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) = 0.6 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) ≤ P(B).]
O No, this is not possible. Since An B is contained in the event B, it must be the case that P(ANB) ≤ P(B). However 0.5 > 0.3 violates this requirement.
O Yes, this is possible. Since AB is contained in the event B, it must be the case that P(B) ≤ P(AB) and 0.5 0.3 does not violate this requirement.
O No, this is not possible. Since B is contained in the event A n B, it must be the case that P(ANB) ≤ P(B). However 0.5 > 0.3 violates this requirement.
O 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.
O Yes, this is possible. Since B is contained in the event A n B, it must be the case that P(B) ≤ P(ANB) and 0.5 > 0.3 does not violate this requirement.
(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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1d22174-c151-4e74-97ee-742f22ff5b0b%2F5dd68909-9b4a-4726-9fb0-15147dd1077a%2F1okv5vk_processed.png&w=3840&q=75)
Transcribed Image Text: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) = 0.6 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) ≤ P(B).]
O No, this is not possible. Since An B is contained in the event B, it must be the case that P(ANB) ≤ P(B). However 0.5 > 0.3 violates this requirement.
O Yes, this is possible. Since AB is contained in the event B, it must be the case that P(B) ≤ P(AB) and 0.5 0.3 does not violate this requirement.
O No, this is not possible. Since B is contained in the event A n B, it must be the case that P(ANB) ≤ P(B). However 0.5 > 0.3 violates this requirement.
O 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.
O Yes, this is possible. Since B is contained in the event A n B, it must be the case that P(B) ≤ P(ANB) and 0.5 > 0.3 does not violate this requirement.
(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?
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