# 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.