1. A student randomly selects classmates from their local community college and ask each how many siblings he/she has. The table below summarizes the data. Construct a probability distribution. Show Work! Number of Siblings (x) Frequency f P(x) 0 9 1 16 2 10 3 4 4 1 2. A survey was conducted that asked participants how many pets were in their household; their responses are recorded below. Construct a probability distribution for this data. Show Work! Pets 0 1 2 3 4 5 Households 941 1349 703 178 67 21 P(x) 3.1 - 3.2 Assignment Name: 2 Use the Addition Rule for Probabilities. Show all work! 3. If A and B are events with P(A)=0.6, P(B)=0.2, P(A AND B)=0.05, find P(A OR B). 4. If A and B are events with P(A)=0.5, P(A OR B)=0.95, P(A AND B)=0.02, find P(B). 5. If the probability of a student taking a math class is 0.50, the probability of taking a history class is 0.30, and the probability of taking a math class and a history class is 0.02, what is the probability of a student taking a math class or a history class 3 Use the Complement Rule for Probabilities. Show Work! 6. 26 blocks are in a bag, all with a letter of the alphabet on them. Answer the following questions:| a. What is the probability that you will not draw the first letter of the alphabet from the bag? b. What is the probability that you will not draw a letter in the word "Mathematics"? c. If the probability of not drawing a group of four letters is 2/9, what is the probability of drawing that group of four letters? Use the Addition Rule for Mutually Exclusive Event Probabilities. Show Work! 7. You draw a single card from a standard deck of cards. Assume a face card is a Jack, Queen, King, or Ace. Find the probability that: a. you draw a King or a Queen. b. you draw a 6 or a 7. c. you draw an even numbered card or a face card. 4 8. A government committee consists of 20 republicans, 18 democrats and 3 independents. If one member is selected at random, what is the probability that he/she is a democrat or an independent? Use the Multiplication Rule for Independent Event Probabilities. Show Work! 9. If A and B are two independent events with ( ) = 0.6 and () = 0.7, calculate () Use Conditional Probability Notation to Describe Events. Show Work! 10. Suppose you roll a die. Let E be the event that the die lands on an even number. Let A be the event that the die lands on 2. a. How would you represent the probability that the die lands on 2, given that it lands on an even number? b. How would you represent the probability that the die lands on 2, given that it lands on an odd number? 5 Create and Interpret Contingency Tables to Find Probabilities. Show Work! 11. The following contingency table looks at a study of the number of engineering majors and non-engineering majors that like and dislike math. Show Work! Students Engineering major Non-engineering major Total Likes Math 46 21 67 Does not like Math 23 55 78 Total 69 76 145 From the above table, what was the probability that: c. a randomly chosen student does not like Math, given that the student in an engineering major? d. a randomly chosen student does not like Math, given that the student in a nonengineering major? e. a randomly chosen student does like Math, given that the student in an engineering major? 6 12. A 2017 study by researchers at a college showed that using a budget was effective at cutting costs while attempting to successfully maintain monthly expenses. Show Work! Participants Cut Costs Did not cut costs Total Given a budget 37 13 50 Not given a budget 3 25 28 Total 40 38 78 From the above table, what was the probability that: a. a randomly chosen participant did not cut costs even after the participant was given a budget? b. a randomly chosen participant did not cut costs even after the participant was not given a budget? c. a randomly chosen participant did cut costs even after the participant was given a budget?