l. A survey among 250 Junior and Senior students in a particular university in Kuwait resulted in the following information. If randomly a student is selected, Year Mathematics Economics Accounting Total Junior 30 25 55 l 10 Senior 140 Total 250 a. What is the probability that a student is taking Mathematics? I). What is the probability that a student is senior and taking Accounting? c. What is the probability that a student is senior or taking Accounting? (1. What is the probability that a student is Junior given That hefshe is taking Economics? 2. A survey conducted by the Sega] Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their compensation packages. For small companies, 43 of the 180 surveyed indicated that they offer stock options as part of their compensation packages to their board members. a. Complete the following contingency table. _ompany Se Total snack Options -- I\" b. What is the probability that the company offered stock options to their board members? What is the probability that the company is small or offered stock options to their board members? (1. What is the probability that a randomly selected company offered stock options to their board members given that it is a large company? a o 3. A sample of 300 adults is selected. The contingency table below shows their registration status and their preferred source of information on current events. If an adult is selected at random, Television Newspapers Radio Internet Total Registered voter 45 30 45 36 156 Not registered voter 35 44 45 20 144 Total 80 74 90 56 300 a. What is the probability that he/she prefers to get his/her current information from the Internet? b. What is the probability that he/she is a registered voter? c. What is the probability that he/she is a registered voter and prefers to get his/her current information from the television? d. What is the probability that he/she is Not a registered voter and prefers to get his/her current information from the Newspapers? e. What is the probability that he/she is a registered voter given that he/she prefers to get his/her current information from the Radio?4. A quality control inspector is checking a sample of lightbulbs for defects. The table summarizes the results. If one of these light bulbs is selected at random Good Defective Total Medium watts High watts 15 55 60 Total 24 176 200 a. What is the probability that the light bulb is defective? I). What is the probability that the light bulb is Defective or high watts? c. What is the probability that the light bulb is good or low watts? d. What is the probability that the light bulb IS good given that it is low watts? 5. Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda (S). 70% of the patrons are males. 15% of the females (F) preferred soda. 80% of the males (M) preferred water (W). 3. Find the probability that a randomly selected patron prefers soda P (S). b. Find the probability that we randomly selected patron is a male given that he prefers water, 6. Assume that a person comes to a movie on time or late. If a person comes the movie on time, there is 80% chance that he will like the movie. If he comes late, there is 40% chance that he will not like the movie. If 30% people are late based on History; a. What is the probability that a randomly selected person liked the movie? I). What is the probability that a randomly selected person was late and did not like the movie? c. What is the probability that a randomly selected person was late given that he liked the movie? 7. At a Texas college, 60% of the students are 'on'i the southern part of the state, 30% are rm: the northern part of the state, and the remaining 10% are from out-ofstate. All students must take and pass an Entry Level Math (ELM test. 60% of the southerners have passed the ELM, 730% of the northemers have passed the ELM, and 90% of the out-of-staters have passed the ELM. 99' What is the probability that a randomly selected student is from northern Texas and didn't pass the ELM? What is the probability that a randomly selected student has passed the ELM? What is the probability that a randomly selected student is from southern Texas given that he passed the ELM? Practice Questions on Counting rules A simple survey consists of three multiple choice questions. The rst question has 3 possible answers, the second has 4 possible answers and the third has 5 possible answers. What is the total number of different ways in which this survey could be completed? How many ways can a company select 3 candidates to interview from a short list of 15? . 0f ve letters (A, B, C, D. E), three letters are to be selected at random. How many possible selections are there? An experiments consists of three steps. There are 5 possible results in the rst step, 4 possible results on the second step and 3 possible results on the third step. How many total number of experiment outcomes are there? 10. a. A student has 6 different books. In how many ways he can arrange these books on a bookshelf? b. A student has 6 different books, but there is room for only 4 books on the shelf, how many ways are there of placing 4 books into the shelf? 11. You are planning to register in 2 Science courses and 3 Math courses next semester. Currently, there are 5 open Science courses and 6 open Math courses. a. HOW many different ways can you choose 2 Science courses? I}. How many different ways can you choose 3 Math courses? c. How many different ways can you choose 2 Science courses and 3 Math courses? d. If you have to take Basic calculus as part of your math courses, how many different ways can you choose 2 Science courses and 3 Math courses? 12. Suppose that you roll a die 2 times. It. Find the number of possible outcomes and list them. What is the probability that the rst die is 3; and the second die is 4? b. e. What is the probability that you get one 3 and one 4? d. What is the probability that their sum is more than 9? 13. Suppose that you toss a fair coin 3 times. a. List all possible outcomes. b. What is the probability that all three are tails? c. What is the probability that only one of them is Head? :1. What is the probability that at least one of them is Head? 14. There are 6 doctors and 8 nurses in a clinic. a. How many different ways can you choose 2 doctors? I}. How many different ways can you choose 3 Nurses? c. How many different ways can you choose 2 doctors and 3 nurses? {1. If the specialist nurse Mrs. X has to he in the Group of 3 Nurses, in how many different ways you can choose 2 doctors and 3 nurses? e. If you randomly choose 5 persons, what is the probability that there are 2 doctors and 3 nurses? 15. If 5 friends (A, B, C, D, E) sit in a row a. How many different ways can they sit? b. How many different ways can they sit such that A sits next to D? c. How many different ways can they sit such that A 3:. D do not sit next to each other