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Material Type: Exam; Class: Probability; Subject: Mathematics; University: University of San Diego; Term: Fall 2007;
Typology: Exams
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Instructions:Answer each question completely and show all work.
Suppose fair 4, 6 , 8 , 12 and 20-sided dice are placed in a bag and selected at random (each of the 5 dice is equally likely to be selected) and then that die is rolled.
(a) What is the probability a 7 is rolled? (b) What is the conditional probability that the 8-sided die was selected given that a 7 is rolled? (c) Suppose that a die selected from the bag and rolled 3 times (so the same die is rolled 3 times). What is the probability that one of the 4-sided dice was chosen given that all 3 rolls are between 1 and 4?
(a) the probability that a randomly selected family owns both a dog and a cat (b) the probability that a randomly selected family owns a dog given that it owns a cat?
(a) Find the probability of that: i. both E 1 and E 2 occur but not E 3. ii. at least one of the events E 1 , E 2 or E 3 occurs. iii. at least one of the events E 1 , E 2 , E 3 or E 4 occurs. iv. exactly two of the four events occur. (b) Give an example of an experiment and four events E 1 , E 2 , E 3 and E 4 that satisfy the above conditions.
You may turn a solutions to this question on Monday, but you cannot talk to other people about it.
P(Ak) =
Prove that: P
k=
Ak
(Hint show that:
P
k=
Ak
for any > 0.