SECTION NUMBER. Check that your exam contains 25 questions numbered sequentially.

Transcription

1 MATH 07 FAKE FINAL EXAM April 20 NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER On your scantron, write and bubble your PSU ID, Section Number, and Test Version. Failure to correctly code these items may result in a loss of 5 points on the exam. On your scantron, bubble letters corresponding to your answers on indicated questions. It is a good idea for future review to circle your answers in the test booklet. Check that your exam contains 25 questions numbered sequentially. Answer Questions -25 on your scantron. Each multiple choice question is worth 6 points. THE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELECTRONIC DEVICE IS NOT PERMITTED IN THIS EXAMINATION. THE USE OF NOTES OF ANY KIND IS NOT PERMITTED DURING THIS EXAMINATION.

2 MATH 07 FAKE FINAL EXAM, PAGE 2. Which of the following is not a statement? + = 0 The light is very dim. Is the carpet brown? I just saw a pink elephant walk down the street! 2. Let Statement A = p (q r), and Statement B = r ( q p). If p = T, q = T, and r = F, then A = T and B = T. A = T and B = F. A = F and B = T. A = F and B = F. 3. Which of the following is the negation of the statement: If the box is too heavy, then you will get hurt? If the box is too heavy, then you won t get hurt. The box is not too heavy or you will get hurt. The box is too heavy and you won t get hurt. If the box is not too heavy, then you won t get hurt.

3 MATH 07 FAKE FINAL EXAM, PAGE 3 4. Which of the following is not equivalent to the statement, If I miss the bus, then I walk to school? I walk to school only if I miss the bus. I walk to school when I miss the bus. If I miss the bus I walk to school. I walk to school if I miss the bus. 5. Given the following argument, which conclusion yields a valid argument? p r r q q s p s s p s p s 6. Let v(x) represent x can vote, let b(x) represent x was born in the US, and let c(x) represent x is an American citizen. Which of the following represents the negation of the statement, All voters were born in the US or are American citizens? x[v(x) ( b(x) c(x))] x[v(x) ( b(x) c(x))] x[v(x) ( b(x) c(x))] x[v(x) ( b(x) c(x))]

4 MATH 07 FAKE FINAL EXAM, PAGE 4 7. Consider the argument: All cats make good pets. Odie is not a good pet. Therefore, Odie is not a cat. Which of the following is true? The argument is valid. The argument is invalid. The argument is neither valid nor invalid. Not enough information to decide. 8. Let U = {x x 20} be the universal set. Let A = {, 4, 5, 7, 8, 2, 4, 6, 9} and B = {8, 4, 5, 7, 9}. Find the set (A B ). {, 4, 5, 6, 2, 6, 9} {8, 4, 9} {2, 3, 6, 8, 9, 0,, 3, 4, 5, 7, 8, 9, 20} {5, 7} 9. In a recent survey of 24 students, 0 said they wore neither glasses nor contacts, 8 said they wore just contacts, and 3 said they wore just glasses. How many students wear both contacts and glasses? 3 6 4

5 MATH 07 FAKE FINAL EXAM, PAGE 5 0. Suppose you roll a fair, 2-sided die. What is the probability that you roll an even number or an number divisible by four? A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is neither red nor a four? What are the odds of drawing a diamond from a standard, 52-card deck? to 4. to 3. 3 to. 3 to 4.

6 MATH 07 FAKE FINAL EXAM, PAGE 6 3. Suppose P (F ) = 3 5 and P (F E) = 0.3. What is P (E F )? You draw two cards (one at a time, without replacement) from a standard deck. What is the probability that you draw two 7 s? Suppose P (E) = 0.5, P (F ) = 0.4, and P (E F ) = 0.7. Which of the following must be true? E and F are both independent and mutually exclusive. E and F are independent, but not mutually exclusive. E and F are not independent, but are mututally exclusive. E and F are neither independent nor mutually exclusive.

7 MATH 07 FAKE FINAL EXAM, PAGE 7 6. At a local restaurant, 20% of dinner-time patrons leave a tip on the table, while 60% of lunch-time patrons leave their tip on the table. Suppose that 40% of the patrons come for lunch. What is the probability that a patron leaves their tip on the table? A local grocery store has two checkout lines: Line A and Line B, which are used equally. Of the people who go through Line A, 75% are men, while 0% of those who use Line B are men. Given that a shopper is female, what is the probability that she used Line B? [Hint: Use Bayes Theorem.] An escaped prisoner of war is trying to make it back to friendly territory by smuggling himself on a train. He has one day to get on a train (if he waits any longer, he will be found and returned to the camp). There are four different train routes that he could take to get home. Each day, four trains depart (one along each route) at 9a.m., 2noon, and 3p.m.. How many options does the POW have to get home?

8 MATH 07 FAKE FINAL EXAM, PAGE 8 9. Ten people are competing in a race and the newspaper only wishes to report the top three finishes. How many possible listings are there? , How many different license plates may be created from the following characters: 5, 7, 7, A, A, A, and Y? , In some new card game, you have 3 cards in your hand, but must select three of them to pass to the person on your right. Suppose your hand consists of the following cards: three K s, two Q s, four 9 s, one 8, one 5, two A s. How many ways are there to pass three cards where exactly one is a King? , 97 98

9 MATH 07 FAKE FINAL EXAM, PAGE Three apples, two bananas, and one orange are in a bowl. What is the probability that, in grabbing two pieces of fruit, the orange is selected? A local farmer is selling eggs packaged by the dozen. He inspects three of the dozen eggs. If he finds a broken one, he does not sell the dozen. Suppose that there are two broken eggs in each dozen. What is the probability that the he sells a given batch of eggs? The twenty-six letters of the alphabet are placed in a box. Four letters are drawn (one at a time, with replacement). What is the probability that the created word ends with TH?

10 MATH 07 FAKE FINAL EXAM, PAGE A box contains the letters s, m, a, l, and l. What is the probability that as they are drawn from the box (one at a time, without replacement), we spell the word SMALL? Chris wins half of his tennis matches. What is the probability that he loses 4 of the next 5 matches? /6 2 /2 5/ Two boys each roll a 6-sided die three times. What is the probability of both boys roll three numbers greater than 4?

11 MATH 07 FAKE FINAL EXAM, PAGE 28. Which one of the following is true? P (20, 2) = 20! 2! ( ) 20 = ( ) 20 P (20, 2) = 2 2 ( ) ( ) = ! 2!8! 3!7! 4!6! 5!5! 6!4! ( ) Let x be a random variable with a probability distribution as given by the following table: x p(x) What is the expected value of x? Aaron and Bob play 8 games of tic-tac-toe. Suppose Bob is a more skilled player and he wins 75% of the time. Find the expected number of wins for Aaron