Chapter 3 Revised Homework Assignment

Use a separate piece of paper and show your work.

Do not try to fit it all on here.Problem #1(Replacement for #80 in the textbook)

The Bible is comprised of 66 books, with 39 books in the Old Testament and 27 books in the New Testament.

Assuming that Paul did not write Hebrews(which can be debated),we can say that 13 of the books in the Bible were written by Paul(and all of them are in the New Testament).

Several of the books in the Bible have a "1st" and "2nd" (and possibly a "3rd") in their titles. Some examples include "1 and 2 Samuel," and "1, 2, and 3 John."In the Old Testament, six out of the thirty-nine books fit in this category. In the New Testament, eleven out of the twenty-seven books fit in this category.

One book of the Bible is selected at random.Assume each book is equally likely to be chosen.

Letbe the event that the author is Paul,be the event that the book is in the Old Testament,be the event that the book is in the New Testament, andbe the event that the book is in thecategory of "books with 1stand 2ndand/or 3rd."

Whenever applicable, show the formula you are using and the specific values you are plugging into the formula. Do not just write the final answer.

Using the information provided in the beginning setup, answer the following questions:

Find().

Find(|).

Find().

Find(|).

Find().

In words, what probability does(|)represent? (i.e. Finish the sentence:"(|)isthe probability that the randomly selected book....).

In words, what probability does()represent?

Find( and ).

In words, what probability does( and )represent?

Find( or ).

Areandmutually exclusive events? Explain why or why not, using probability.

Problem #2(Replacement for #88 in the textbook) An experiment consists of first tossing a coin and then rolling a die.

List the sample space for this experiment.

Letbe the event that the coin lands on "heads" and anumber greater than 4 is rolled on

the die. Find().

Letbe the event that the coin lands on"tails" and an even number is rolled on the die.

Find().

Areandmutually exclusive events? Explain your answer,using probability.

Problem #3(Replacement for #100 in the textbook)

At a certain college, 38% of the students are full-time students and 62% are part-time students. Of all the students at the college, 37.4% have taken at least one evening class. Also, 45% of the part-time students have taken at least one evening class, and 25% of the full-time students have taken at least one evening class.

A student at this college is selected at random. Letbe the event that the student is part-time. Letbe the event that the student has taken at least one evening class.

For each part, show the formula you are using and the specific values you are plugging into the formula. Do not just write the final answers.

Find( and ).

Find(|).

Find( or ).

Areandindependent? Explain your reasoning,using probability.

Areandmutually exclusive? Explain your reasoning,using probability.

Problem #4(Replacement for #122 in the textbook) Suppose that you have twelve cards. Four are red and eight are blue. The cards are well-shuffled.

From this set of cards, two cards are selected at random, one at a time,without replacement.Let1be the event that the 1stcard drawn is Red. Let2be the event that the 2ndcard drawn is Red. Let1and2be defined the same way, using Blue instead of Red.

Show the appropriate calculation for each part. Do not just write the final answers.

Draw a tree diagram of the situation, including appropriate numerical values on each branch.

Find(1and2).

Find(at least one red card is drawn).

Find(2|1).

Are1and2independent events? Explain why or why not.

Problem #5(Replacement for #124 in the textbook) The percent of U.S. drivers (from a recent year) that are female is 49.75. Of the females,

4.97% are age 19 and under

80.20% are age 20-64

14.83% are age 65 or over

Of the licensed U.S. male drivers,

5.25% are age 19 and under

80.90% are age 20-64

13.85% are age 65 or over

(Source accessed 8/21/2019:https://www.fhwa.dot.gov/ohim/onh00/bar7.htm)Suppose that 16,000 U.S. licensed drivers are randomly selected.

How many would you expect to be male?Show your calculation.

Construct a contingency table of gender versus age group.

Using the contingency table, find the probability that out of the "age 19 and under" agegroup, a randomly selected driver is male.Show your calculation.