1. Six boys have to form two 3 men's basketball teams. If any choice is equally likely, the probability that the 3 Bellamonica brothers play together in any of the two teams is ( ) 1 1 20 63 (A) (A) 10 2. Let A and B be two independent events. Which of the following statements is false? ( ) (A) P((AUB)) = 1 [P(A) + P(B)] (C) P(An B) = P(A)P(B) (C) 3. During the exam of Statistics 50 students are seated in a 50 seats-Lab along 10 rows with an equal number of computer stations. There are 4 versions of the exam that are randomly and independently selected by the computer and assigned to the students. The probability that the students in the first row receive the same version of the exam is ( ) 4 (A) 50 4 16 17 8 9 (A) P(AUB) = (C) P(AUB) = (B) 4. The probability that a signal frequency is less than 70MHz is equal to 2. In such a case a 3 message is correctly received in the 80% of the signals, otherwise if the frequency is equal or greater than 70MHz, the same percentage falls to 10%. If the signal is correctly received, then the probability the frequency us less than 70MHz is ( ) 6 2 (A) (C) (B) 3 (C) 4 5 (B) P(A/B) = P(A) (D) P(AB) = 1 - P(A) 21 3 (C) (B) 5. Three different letters are chosen at random from an alphabet containing 40 letters, of which 25 are small and 15 capital. The probability of choosing at least one capital letter is () (A) 0.767 (B) 0.455 D) ( 6. Let A and B be two events such that P(A) = 1, P(B) = 1 and P(B|A) = 1. Then ( ) 5 (D) 32 33 17 25 (C) 1 - ( (B) P(AUB) = (D) (D) P(AUB) = 1 60 23 30 5 (D) 6 (B) 7. Let S = {1, 2, 3, 4, 5, 6, 7, 8} be a uniform probability space and consider the events A = {1,2,3,4}, B = {1,2,5, 6} and C= {3, 4, 5, 6}. Which of the following statement is true? ( ) (A) A, B and C are pairwise disjoint (B) A, B and C are independent 4 450 (C) A, B and C are not independent (D) None of the previous statements is true 8. The number of strictly increasing 3 digit sequences is (where each digit is between 0 and 9) ( ) (A) 720 (B) 120 (C) 30 (D) 10 9. Let A and B two events such that P(A) = 1/3, P(B) = 5/12 and P(B|A) = 1/2. Then ( ) (A) P(AB) = 1/3 (B) P(AUB) = 1/2 (C) P(An B) = 1/4 (D) P(AUB) = 3/4 10. A basket contains 3 red balls, 2 green balls and 2 blue balls. Two of them are extracted, without replacement. The probability of extracting two of the same color is ( ) 10 49 (D) none of the other statements is correct Problems (20' x 4 = 80') 1. Compute the probability that the winning number in roulette (check the roulette in wikipedia) is: (a) between 6 and 12 (included) or strictly greater than 25; (b) a multiple of 6 or a multiple of 7; (c) greater or equal to 18 or a multiple of 3.