OLSON
Sample Test
(1) Create a table and a Venn Diagram for the following:
Of 22 elements, 5 are in X but outside Y, 10 are in Y but outside X, and 2 and are neither X nor Y.
(2) U= {a, c, e, g, i, k, m, o, s, t}, X: {a, c, i, m, s}, Y: {a, e, g, m}
(a) X∩Y? (b) n(XcUY) (c) (XUY)c (d) X∩Yc
(3) Complete the Venn Diagram for:
n(U)=30, n(R)=14, n(S)=11=n(T), n(R∩S)=5, n(R∩T)=4, n(S∩T)=3, n(RUSUT)c=5.
(4) 31 pizza eaters revealed their topping preferences. 16 like Liver (L), 16 like Strawberries (S), 12 like Anchovies (A). Also, 10 like Strawberries and Anchovies, while 4 like Liver and Strawberries and 4 like Liver and Anchovies. If 3 like none of these toppings, complete the Venn Diagram.
(5) 6 people line-up for a photograph, but 2 of them MUST sit next to one another. How many possible line-ups are there?
(6) A test consists of 8 true-false questions. How many different keys are possible?
(7) How many 3-digit numerals can be formed from {2, 3, 5, 6, 8, 9}, with the following restrictions:
(a) no restriction, repeats allowed (b) an even digit, no repeats
(c) a number less than 600 with repeats (d) a number divisible by 5, no repeats
(8) If an experiment is a coin tossed and a die tossed. What are the elements from the sample space created by this above experiment for…
(a) when the coin is a tail. (b) when the coin is a head and the die is less than 3
(9) Draw a tree diagram for the case where Sam brings Pam back home. He will either kiss her or shake her hand; and her response will be to faint or sigh.
What is the sample space?
(10)
Event / Bad / Poor / Average / Good / GreatProbability / 0.20 / 0.10 / 0.15 / 0.25
What is the probability for:
(a) at least Average (b) at most poor (c) not great or poor