# Answer the following questions True or False. Assume we are using the

Answer the following questions True or False. Assume we are using the Law of Excluded Middle. Each question is worth 1 point. You may assume Events are special types of sets. (12)
According to our discussion on logic, the law of excluded middle means that for any logical
statement, S, that is True, then Not S can sometimes be True? T F
For Events A, B: The General Addition Law is: P(A or B) = P(A) + P(B) – P(A and B)? T F
Union for two sets is the same as when we “OR” two Events? T F
Intersection for two sets is the same as when we “OR” two Events T F
For any event E: P(E) + P(Not E) = 1? T F
If E, F are Events then an example of a compound Event is ( E OR F )? T F
One interpretation for the meaning of a probability of an event is that the probability
represents the frequency an event can be expected to occur over many repeated trials
or repetition of the same action ? T F
A sample space, S, contains all possible outcomes which can occur? T F
S is the sample space, E is an event, then in an equally likely or Fair system
P(E) = #E/#S? T F
The probability of an event E, P(E), can be any number such that: -1 ≤ P( E) < 1 T F A truth table shows the possible truth values for any logical statement? T F Let “E” be an event, if P(E) = 0 then we say this is an impossible event. T F Fill in the following Truth Tables (3) (1) M Not M (2) M N M AND N M OR N Go to the next page Your friend has written a computer program that simulates the roll of a fair 8-sided die. Let the sample Space = S = {1, 2, 3, 4, 5, 6, 7, 8 } represent the set of all possible outcomes on a roll of the die. (10) Define the following Events: A = { 2, 4, 6, 8} B = {1, 3, 5, 8} C = { 1, 2, 5, 7 } D = { 2, 6, 7} Find the following Events. Each is worth 1 point. (5) A OR B = { }? B AND C = { } ? Not C = { } ? A AND C = { } ? B AND D = { } ? Use the equally likely formula for any event E: P( E) = #E/#S and find: One pt. each. (5) P(A or B) = P(B And C ) = P(Not C) = P(A and C) = P(Not (B and D) ) Bob wishes to kick back and relax after a long week of exams and studying. He has 3 bathrobes, 4 pairs of pajamas, 2 pairs of slippers, 3 blankets, and 2 comfortable chairs to sit back and relax in. How nay ways can Bob kick back and just relax? (1) You have 7 students who apply for 2 jobs. How many ways can you select 2 students from the 7 to fill the 2 identical jobs? (1) You have 7 students who apply for 2 student grants. The first grant is worth \$10,000 and the second grant is worth \$5,000. How many ways can you select the 2 student scholarship winners from the 7 ? (1) You have purchased two stocks, stock A and stock B. You have been using a stock trending and evaluation software to try and predict if your stock will increase in value by the end of the month and enter several “Key Market Performance Indicators” into the program. It returns the following end of the month predictions to you. The probability stock A will increase in value is, P (A) = 0.4, the probability stock B will increase in value is, P(B) = 0.5, and the probability both will increase in value is, P( A and B) = 0.2. What is the probability that (stock A OR stock B) increases in value, P( A OR B)?