Question

1. (Floyd, Chapter 2, problem 1) Suppose a random process has a total of three basic outcomes: o1, o2 and o3. In other words, its sample space is S = {o1, o2, o3}. The probabilities of o2 and o3 are 0.5 and 0.4 respectively. Let E be the event consisting of basic outcomes o2 and o3—that is, even E is said to occur if either o2 or o3 occurs. The probability of the complementary event to E is: (a) .1 (b) .9 (c) .8 (d) .2 (e) none of the above. 2. (Floyd, Chapter 2, problem 2) Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. Determine the probability of observing the following events. (a) Two blue marbles are drawn. (b) A red and a blue marble are drawn. (c) Two red marbles are drawn. 3. (Floyd, Chapter 2, problem 13) A club has 100 members, 40 of whom are lawyers and 30 of whom are liars. A total of 60 members are neither lawyers nor liars. Out of all the club's lawyers, what proportion are liars? (Hint: To start your answer, draw a Venn diagram) 4. (Floyd, Chapter 2, problem 3) Three events A, B, and C are defined over some sample space S. Events A and B are independent. Events A and C are mutually exclusive. Some relevant probabilities are Pr(A) = .04, Pr(B) = .25, Pr(C) = .2 and Pr(B|C) = .15. Compute the values of Pr(A ? B), Pr(A ? C), Pr(A ? B ? C) and Pr(C|B). 5. (Floyd, Chapter 2, problem 4) A sample space S contains a total of five possible outcomes (?elementary events?) denoted by {s1, s2, s3, s4, s5} with associated probabilities of occurrence {.22, .31, .15, .22, .10}. The following events are defined: E1 = {s1, s3}; E2 = {s2, s3, s4}; and E3 = {s1, s5}. Find each of the following probabilities: (a) Pr(E1) (b) Pr(E2) (c) Pr(E1 ? E2) (d) Pr(E1|E2) (e) Pr(E2 ? E3) and (f) Pr(E3|E2).

          1. (Floyd, Chapter 2, problem 1) Suppose a random process has a total of three basic outcomes: o1, o2 and o3. In other words, its sample space is S = {o1, o2, o3}. The probabilities of o2 and o3 are 0.5 and 0.4 respectively.
Let E be the event consisting of basic outcomes o2 and o3—that is, even E is said to occur if either o2 or o3 occurs. The probability of the complementary event to E is: (a) .1 (b) .9 (c) .8 (d) .2 (e) none of the above.

2. (Floyd, Chapter 2, problem 2) Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. Determine the probability of observing the following events. (a) Two blue marbles are drawn. (b) A red and a blue marble are drawn. (c) Two red marbles are drawn.

3. (Floyd, Chapter 2, problem 13) A club has 100 members, 40 of whom are lawyers and 30 of whom are liars. A total of 60 members are neither lawyers nor liars. Out of all the club's lawyers, what proportion are liars? (Hint: To start your answer, draw a Venn diagram)

4. (Floyd, Chapter 2, problem 3) Three events A, B, and C are defined over some sample space S. Events A and B are independent. Events A and C are mutually exclusive. Some relevant probabilities are Pr(A) = .04, Pr(B) = .25, Pr(C) = .2 and Pr(B|C) = .15. Compute the values of Pr(A ? B), Pr(A ? C), Pr(A ? B ? C) and Pr(C|B).

5. (Floyd, Chapter 2, problem 4) A sample space S contains a total of five possible outcomes (?elementary events?) denoted by {s1, s2, s3, s4, s5} with associated probabilities of occurrence {.22, .31, .15, .22, .10}. The following events are defined: E1 = {s1, s3}; E2 = {s2, s3, s4}; and E3 = {s1, s5}.
Find each of the following probabilities: (a) Pr(E1) (b) Pr(E2) (c) Pr(E1 ? E2) (d) Pr(E1|E2) (e) Pr(E2 ? E3) and (f) Pr(E3|E2).

1. (Floyd, Chapter 2, problem 1) Suppose a random process has a total of three basic outcomes: o1, o2 and o3. In other words, its sample space is S = o1, o2, o3. The probabilities of o2 and o3 are 0.5 and 0.4 respectively.
Let E be the event consisting of basic outcomes o2 and o3—that is, even E is said to occur if either o2 or o3 occurs. The probability of the complementary event to E is: (a) .1 (b) .9 (c) .8 (d) .2 (e) none of the above.

2. (Floyd, Chapter 2, problem 2) Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. Determine the probability of observing the following events. (a) Two blue marbles are drawn. (b) A red and a blue marble are drawn. (c) Two red marbles are drawn.

3. (Floyd, Chapter 2, problem 13) A club has 100 members, 40 of whom are lawyers and 30 of whom are liars. A total of 60 members are neither lawyers nor liars. Out of all the club's lawyers, what proportion are liars? (Hint: To start your answer, draw a Venn diagram)

4. (Floyd, Chapter 2, problem 3) Three events A, B, and C are defined over some sample space S. Events A and B are independent. Events A and C are mutually exclusive. Some relevant probabilities are Pr(A) = .04, Pr(B) = .25, Pr(C) = .2 and Pr(B|C) = .15. Compute the values of Pr(A ? B), Pr(A ? C), Pr(A ? B ? C) and Pr(C|B).

5. (Floyd, Chapter 2, problem 4) A sample space S contains a total of five possible outcomes (?elementary events?) denoted by s1, s2, s3, s4, s5 with associated probabilities of occurrence .22, .31, .15, .22, .10. The following events are defined: E1 = s1, s3; E2 = s2, s3, s4; and E3 = s1, s5.
Find each of the following probabilities: (a) Pr(E1) (b) Pr(E2) (c) Pr(E1 ? E2) (d) Pr(E1|E2) (e) Pr(E2 ? E3) and (f) Pr(E3|E2).

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