Consider the following compound statement: If Robert studies for the exam and gets a good night sleep, then Robert will do good on the exam.

Transcription

1 MTH107 Intro. to Finite Math: Fall 2013 Final Review worksheet. December 4, 2013 NAME: Chapters 1 and 2 Review Consider the syllogism: All students love math. Larry is a student. Larry loves math. 1. List and label the major and minor premise. 2. Is the syllogism valid? Consider the following compound statement: If Robert studies for the exam and gets a good night sleep, then Robert will do good on the exam. 3. How many statements are there? 4. What type of statement is the compound statement? 5. Write the compound statement in symbolic form. 6. Construct a Truth Table for the compound statement.

2 7. Complete the following truth table. p q p q p q q p p q q p T T F T F F T F F 8. From the conditionals in question 1., which are equivalent? 9. Let p q be a given conditional. Label the following as: the inverse, the converse, or the contrapositive. q p p q q p

3 Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} be the universal set. Let A = {2, 3, 7, 8, 9}, and B = {0, 1, 4, 5, 9}. 10. Find A B. 11. Find A B. 12. Find n(a B). 13. Find n(a B ). ) 14. Find n ((A B).

4 3.1 / 3.2 / 3.3 Review An urn contains colored jelly beans: 10 blue, 6 green, 13 white, 7 yellow, 2 red, 12 black. 1. Find the probability of picking each color individually. blue green white yellow red black 2. Find the odds of picking each color individually. blue green white yellow red black 3. Find the probability of picking the following. blue or green white and yellow not red black, red, or green 4. Find the odds of picking the following. blue or yellow white and green not white black, yellow, or green

5 5. A single, six-sided, fair die is rolled. What is the probability that the number that lands face up is divisible by 3? 6. A single, six-sided, fair die is rolled. What is the probability that the number that lands face up is odd or divisible by 2? 7. Two fair dice are rolled. What is the probability that the two faces add to more than 4? 8. Two fair dice are rolled. What is the probability that the two faces do not add to 8? 9. Two fair dice are rolled. What is the probability that the two faces multiply to a negative number? 10. Two fair dice are rolled. What is the probability that the two faces multiply to a positive number?

6 3.4 / 3.6 / 3.7 Review Find the following: 1. The probability of matching an ordered string of six numbers, chosen with replacement, from the numbers The probability of matching four of an ordered string of five numbers, chosen without replacement, from the numbers The probability of being dealt 3 jacks in five card draw. 4. The probability that the second card dealt is a 7 given that the first is a The probability that the first and second card dealt are both 8 s. 6. The probability of being dealt five spades in five card draw. 7. The probability of rolling a 3 given that the roll is odd. 8. The probability of rolling an even given that the roll is a The probability of rolling an even given that the roll is a The probability of being dealt a full house (three of a kind and two of a different kind) in five card draw.

7 people apply for a 6 person committee. 12 are women, 18 are men. 4 are polliticians, 12 are city workers, the rest work in private industry. a) What is the size of the sample space? b) How many ways can 2 men and 4 women make up the committee? c) How many ways can 2 politicians, 3 city workers, and 1 private industry workers make up the committee? d) If the committee is chosen at random what is the probability that the committee is all women? e) If the committee is chosen at random what is the probability that the committee has no politicians? f) If the committee is chosen at random what is the probability that the committee is all men? g) If the committee is chosen at random what is the probability that the committee is either politicians or private industry workers?

8 Chapter 4 review. Complete the following frequency distribution for the given sample. Data point Frequency Relative Frequency Create a grouped frequency distribution for the sample using five groups; find the relative frequency for each group. Data point range Frequency Relative Frequency 2. Find the mean, median, and mode for the sample. 3. Find the standard deviation of the sample. 4. What percentage of the sample lies within one standard deviation of the mean?

9 Given a standard normal distribution, find: 5. p(0.53 < z < 1.41) 6. p( 0.67 < z < 1.23) 7. p(z < 2.06) 8. p( 1.31 < z < 0.36) Given a standard normal distribution, find: 9. p(c < z < 0) = p( c < z < c) = p(z < c) = p(z > c) = A population is normally distributed with standard deviation 2.5 and mean 36.8; find the following probabilities. 13. p(38.4 < x < 40.3) 14. p(32.4 < x < 37.1) 15. What value will place in the bottom 40% of the population? 16. What value will place in the top 15% of the population?