Need Solution for this Statistic Paper

1. Male and Female students at a high school were surveyed about their career preferences. The data are shown in the table below.

a. What is the probability that a randomly selected student wants to be an Engineer?

b. What is the probability that a randomly selected student is a Female and wants to be a Doctor?

c. What is the probability that a randomly selected student wants to be a Doctor or Male?

d. What is the probability that a randomly selected student wants to be an Engineer given that he is Male?

2. The contingency table below shows the statistics for 300 students distributed over three different majors (business, management and finance). If a student is selected at random,

a. What is the probability that he/she is Freshman and he/she is a Finance major?

b. What is the probability that he/she is Freshman and he/she is not a Finance major?

c. What is the probability that he/she is a Management major or he/she is Sophomore?

d. What is the probability that he/she is a Management major given that he/she is Junior?

3. 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,

a. What is the probability that is student is taking Mathematics?

b. What is the probability that is student is senior and taking Accounting?

c. What is the probability that is student is senior or taking Accounting?

d. What is the probability that is student is Junior given That he/she is taking Economics?

4. A survey conducted by the Segal 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.

b. What is the probability that the company offered stock options to their board members?

c. What is the probability that the company is small or offered stock options to their board members?

d. What is the probability that a randomly selected company offered stock options to their board members given that it is a large company?

5. 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,

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?

6. 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

a. What is the probability that the light bulb is defective?

b. What is the probability that the light bulb is Defective or high watt?

c. What is the probability that the light bulb is good or low watt?

d. What is the probability that the light bulb is good given that it is low watts?

7. 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).

a. 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,

8. An airport screens bags for Forbidden Items (FI), and an alarm is supposed to be triggered when a FI is detected. Suppose that 5% of bags contain FI. If a bag contains a FI, there is a 98% chance that it triggers the alarm. If a bag doesn't contain a FI, there is an 8% chance that it triggers the alarm.

a. Draw a contingency table?

b. Find the probability that a randomly selected bag contains a FI and triggers the alarm

c. Given that a randomly chosen bag triggers the alarm, what is the probability that it contains a FI?

9. 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?

b. 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?

10. Students in a certain community were surveyed. Among these students, 60% indicated that they have a laptop. Of those that have a laptop, 90% have a smartphone. Of those that do not own a laptop, 30% have a smartphone.

a. Fill in the contingency table

b. If a student is chosen at random, what is the probability that the student has a laptop?

c. If a student is chosen at random, what is the probability that the student has a laptop and smartphone?

d. If a student is chosen at random, what is the probability that the student does not have a laptop and has a smartphone?

e. What is the probability that the student has a laptop given that he/she has a smartphone?

11. At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.

a. What is the probability that a randomly selected student is from northern Texas and didn’t pass the ELM?

b. What is the probability that a randomly selected student has passed the ELM?

c. What is the probability that a randomly selected student is from southern Texas given that he passed the ELM?

Practice Questions on Counting rules

12.

a. A simple survey consists of three multiple choice questions. The first 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?

b. How many ways can a company select 3 candidates to interview from a short list of 15?

13.

a. Of five letters (A, B, C, D, E), three letters are to be selected at random. How many possible selections are there?

b. An experiments consists of three steps. There are 5 possible results in the first step, 4 possible results on the second step and 3 possible results on the third step. How many total number of experiment outcome are there?

14.

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?

15. An inspection team of 3 lawyers is to be chosen from a candidate pool of 7 lawyers. How many different ways can this team of 3 be formed?

16. 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?

b. 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?

17.

a. A team is being formed that includes 11 different people. There are different positions on the team. How many different ways are there to assign the 11 people to the 11 positions?

b. A student has 9 course books that she would like to place in her backpack. However, she only has room for 3 books. Regardless of the arrangement, how many ways are there she can select 3 books into her backpack?

18. Suppose that you roll a die 2 times.

a. Find the number of possible outcomes and list them.

b. What is the probability that the first die is 3; and the second die is 4?

c. What is the probability that you get one 3 and one 4?

d. What is the probability that their sum is more than 9?

19. 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?

d. What is the probability that at least one of them is Head?

20. There are 6 doctors and 8 nurses in a clinic.

a. How many different ways can you choose 2 doctors?

b. How many different ways can you choose 3 Nurses?

c. How many different ways can you choose 2 doctors and 3 nurses?

d. If the specialist nurse Mrs. X has to be 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?

21. 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 & D do not sit next to each other?