Problem 4. (2.5 %) Which of the following statement is NOT true?
(A) If A ⊂ B, then P(A）≤ P(B）.
(B) If P(B）＞ 0, then P(A|B) ≥ P(A）.
(C) P(A∩B) ≥ P(A）+P(B） - 1.
(D) P(A∩B^c) = P(AUB) - P(B）.

（ ）（3）假使真的發射核子武器，對受影響區域而言，可能衍生出什麼樣的安全威脅是對民生的直接影響？

（ ）（4）雖然本事件與我國看似沒有直接關係，但除了上述可能的威脅外，仍潛藏著什麼樣的安全威脅？

複選題（ ）（1）傳統安全

複選題（ ）（2）非傳統安全

Problem 5. (2.5 %) We toss two fair coins simultaneously and independently. If the outcomes of the two coins are the same, we win； otherwise we lose. Let A be the event that the first coin comes up heads, B be the event that the second coin comes up heads, and C be the event that we win. Which of the following statements is false? (A) Events A and B are independent. (B) Events A and C are not independent. (C) Events A and B are not conditionally independent given C. (D) The probability of winning is 1/2.

Problem 6. (2.5 %o) Suppose X, Y and Z are three independent discrete ran- dom variables. Then X and Y + Z are. _____ independent. (A) always(B) sometimes (C) never 

Problem 7. (2.5 %) Consider two random variables X and Y, each taking values in {1,2,3}. Let their joint PMF be such that for any 1 ≤ x,y ≤ 3, Then, (A) X and Y can be independent or dependent depending upon the strictly positive values (B) X and Y are always independent (C) X and Y can never be independent

Problem 8. (2.5 %o) We throw n identical balls into m urns at random, where each urn is equally likely and each throw is independent of any other throw. What is the probability that i-th urn is empty? (A) (B)(C) (D)

Problem 9. (2.5 %) For a biased coin, the probability of 'heads" is 1/3. Let h be the number of heads in five independent coin tosses. What is the probability P(first toss is a head | h = 1 or h = 5)?(A) (B)(C) (D)

Problem 10. (2.5 %) A well-shuffled deck of 52 cards is dealt evenly to two players (26 cards each). What is the probability that player 1 gets all the cases (A) (B)(C)(D)