# Mutually Exclusive events, Probabilities, and Binomial Distribution

1. Are the events mutually exclusive (Yes or No)?

Event A: Randomly select a person between 18 and 24 years old.

Event B: Randomly select a person that drives a convertible.

2. Decide if the events are mutually exclusive.

Event A: Randomly select a person who uses email.

Event B: Randomly select a person that uses social networking.

Use the table below to answer questions 3-7. The table below shows the number of male and female students enrolled in nursing at a university for a recent semester. Find the specified probability.

Nursing Majors

Nursing Majors Non-Nursing Majors Total

Males 203 1305 1508

Females 841 1498 2339

Total 1044 2803 3847

3. The student is male or a non-nursing major.

4. The student is female or a nursing major.

5. A student is not male or a nursing major.

6. The student is male or a nursing major.

7. Are the events "being male" and "being a nursing major" mutually exclusive?

8. Perform the indicated calculation. 24P5

9. In order to conduct an experiment, 9 subjects are randomly selected from a group of 25 subjects. How many different groups of nine subjects are possible?

Use the information below to answer questions 10 - 11. A combination lock has 5 programmable digits. The first digit may be set to whole number values from 1 to 5. The last four digits may be set to whole number values

from 0-9.

10. How many lock combinations are possible if there are no restrictions?

11. What is the probability of selecting a combination code at random that ends with an odd

number?

12. Determine if the random variable x is discrete or continuous. Explain the reason for

your answer. x is the time required for workers at a factory to complete a task.

Use the frequency distribution below to answer questions 13-17. The number of school-related extracurricular activities per student.

Extracurricular Activities

Activities 0 1 2 3 4 5 6 7

Students 24 33 46 57 63 36 20 14

13. Use the frequency distribution to construct a probability distribution.

14. What is the mean of the probability distribution?

15. What is the variance of the probability distribution?

16. What is the standard deviation of the probability distribution?

17. Interpret the results in the context of the real-life situation

18. A state lottery randomly chooses 6 balls numbered 1 from 1 to 40. You choose 6

numbers and purchase a lottery ticket. The random variable represents the number of matches

on your ticket to the numbers drawn in the lottery. Is this experiment a binomial experiment? Explain your answer.

Use the characteristics of the binomial distribution given below to answer questions 19-21. Suppose there is a binomial distribution with: n = 63 and p = 0:38.

19. What is the mean of the binomial distribution?

20. What is the variance of the binomial distribution?

21. What is the standard deviation of the binomial distribution?

Use the characteristics of the binomial experiment below to answer questions 22-24. Travel Plans Seventeen percent of married couples say they are planning a trip to Europe. You randomly select 15 married couples and ask each if they are planning to travel to Europe.

22. What is the probability that exactly 1 couple says they plan to travel to Europe?

23. What is the probability that more than 1 couple say they plan to travel to Europe?

24. What is the probability that at most 2 couples say they plan to travel to Europe?

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#### Solution Preview

1. Are the events mutually exclusive (Yes or No)?

Yes since there is no relationship between A and B.

2. Decide if the events are mutually exclusive.

No since email is part of the media for the social networking.

3. The student is male or a non-nursing major.

The total for either male or non-nursing major: 203+2803=3006.

The probability=3006/3847=0.7814

4. The student is female or a nursing major.

The total for either female or a nursing major: 1498+1044=2542

The probability=2542/3847=0.6608

5. A student is not male or a nursing major.

The total for either not male or a nursing major: 2339+203=2542

The total probability=2542/3847=0.6608

6. The student is male or a nursing major.

The total for either male or a nursing major: 1508+841=2349

The total probability=2349/3847=0.6106

7. Are the events "being male" and "being a nursing major" mutually exclusive?

These two events are not mutually exclusive since some males are in a nursing major.

8. Perform the indicated ...

#### Solution Summary

The expert determines whether events are mutually exclusive.

Business Statistics: Probability Sample Questions

See the attached file.

Chapter 5

1. Mutually exclusive events cannot be independent.

2. The probability of an event is always greater than zero and less than 1.

3. If events A and B are independent, then the probability of A given B, that is, P(A|B) is equal to 0. F

4. Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as independent events.

5. Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as independent events

6. In a binomial distribution the random variable X is continuous.

7. The variance of the binomial distribution is √np(1-p).

8. The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and the probability of success on any trial must be the same.

9. The mean and variance are the same for a standard normal distribution.

10. In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is discrete.

11. For a discrete random variable which can take values from 0 to 150, P(X ≤ 100) is greater than P(X<100).

12. The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

13. All continuous random variables are normally distributed.

1. Two mutually exclusive events having positive probabilities are ______________ dependent.

A. Always

B. Sometimes

C. Never

2. ___________________ is an event which is .mutually exclusive and collectively exhaustive.

A. Random experiment

B. Sample Space

C. Probability

D. A complement

E. A population

3. In which of the following are the two events A and B, always independent?

A. A and B are mutually exclusive

B. The probability of event A is not influenced by the probability of event B

C. The intersection of A and B is zero

D. Events A and B have no common element

E. B and D

4. If two events are mutually exclusive, we can _____ their probabilities to determine the union probability.

A. Divide

B. Add

C. Multiply

D. Subtract

5. Events that have no sample space outcomes in common and therefore, cannot occur simultaneously are:
A. Independent

B. Mutually Exclusive

C. Intersections

D. Unions

6. If p =.1 and n =10, then the corresponding binomial distribution is

A. Right skewed

B. Left skewed

C. Symmetric

D. Bimodal

7. If p=.55 and n=10, then the corresponding binomial distribution is A. Right skewed B. Left skewed C. Symmetric D. Bimodal

8. The variance of the binomial distribution is equal to: A. P B. Np C. Px(1-p)n-x D. (n)(p)(1-p) E.

9. Which of the following is a not a valid probability value for a discrete random variable? A. .5 B. 1.0 C. -.7 D. 0

10. Which of the following statements about the binomial distribution is not correct? A. Each trial results in a success or failure B. Trials are independent of each other C. The probability of success remains constant from trial to trial D. The random variable of interest is discrete E. All of the above are correct

11. Which one of the following statements is not an assumption of the binomial distribution? A. Sampling is with replacement B. The experiment consists of n identical trials C. The probability of success remains constant from trial to trial D. Trials are independent of each other E. Each trial results in one of two mutually exclusive outcomes

12. A coin is tossed 12 times. What is the probability that more than four heads will occur A. .1938 B. .8062 C. .1208 D. .1934

13. In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that less than 4 of them were laid off. A. .8497 B. .6496 C. .2001 D. .2668

14. The area under the normal curve between z=0 and z=1 is ________________ the area under the normal curve between z=1 and z=2. A. Less than B. Greater than C. Equal to D. A, B or C above depending on the value of the mean E. A, B or C above dependent on the value of the standard deviation

15. The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 904 grams? A. .8849 B. .3849 C. .1151 D. .7698 E. .2302

16. The normal approximation of the binomial distribution without continuity correction is appropriate when: A. np ≥ 10 B. n(1-p) ≥ 10 C. np ≤ 10 D. np(1-p) ≥ 10 E. np≥ 10 and n(1-p)≥ 10

1. At a college, 70 percent of the students are female and 40 percent of the students receive a grade of C. About 45 percent of the students are female and not C students. Use the attatched contingency table.

If a randomly selected student is a C student, what is the probability the student is male? 0.28

2. A and B are independent events. Moreover, P(A) = 0.5 and P(B) = 0.6. Determine P(A B), that is, P(A or B)

3. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 14 calculators are selected at random, what is the probability that 4 or less of the calculators will be defective?

4. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the probability is 0.60 that troubles in a residential service can be repaired on the same day. For the first seven troubles reported on a given day, what is the probability that 4 or more troubles will be repaired on the same day?

5. Given the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it: Between 48 feet and 53 feet?

6. If x is a binomial random variable where n=100 and p=.5, find the probability that x is more than or equal to 45 using the normal approximation to the binomial.

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