Be warned! This assignment is insanely long, and covers Lessons 6 through 9 in my book.  Don't leave it to the last minute.  You probably should break it up, studying a specific lesson, then tackling the relevant questions in the assignment, rather than trying to learn all the lessons before you begin the assignment.

Did you read my tips on how to study and learn this course?  If not, here is a link to those important suggestions:

Did you miss my Tips for Assignment 1? Click here.

The department posted SOLUTIONS for Assignment 1 (these are not my solutions). Click here.

Did you miss my Tips for Assignment 2? Click here.

The department posted SOLUTIONS for Assignment 2 (these are not my solutions). Click here.

Here is a link to the actual assignment, in case you don't have it handy:

Please note that I made major changes to my book in September 2014.  If you are using a book older than September 2014, you are missing about 100 pages of new material and an entirely new lesson on Probability.

Study Lesson 6: Introduction to Probability, Lesson 7: Discrete Probability Distributions, Lesson 8: Inferences about Proportions, and Lesson 9: Chi-Square Tests in my book (if you have it) to prepare for this assignment.  

Remember my advice in the tips above.  Don't start working on the assignment too soon.  Study and learn the lesson first, and use the assignment to test your knowledge.  Of course, always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment.  Learn first, then put your learning to the test.

This is using the methods I teach in Lesson 6.  I suggest that you construct the whole sample space to prepare to answer all the questions in this section.  You could use a tree diagram since you have to account for the fact that you are sampling without replacement, and a tree allows you to track what was picked the first time.  Personally, however, I would make a two-way table, since that is so much easier to construct, then you can simply discard outcomes that are impossible.

Hint: You don't have to label "1" twice. The fact that there are two balls labeled "1", just increases the probability that you would select a ball with the number "1" on it.  I would merely make a 3 by 3 table labeled 1,2,3 along the top and down the side, producing 9 outcomes.  However, one of those outcomes, for example, would be "22" which we know is impossible, because, if you picked "2" the first time, you couldn't pick "2" the second time, too, since there was only one "2" ball.  On the other hand, "11" is possible, since there are two "1" balls.  When it comes time to computing the probabilities for each outcome, keep in mind that the first selection is choosing from four balls, but the second selection has only three balls left to choose from.  See my Lesson 6, #13 for a good example.

Remember, you are merely asked for the number of outcomes in the sample space, not the actual sample space.

I recommend that you first compute the probability distribution for the sample space found in question 1 above.  Then, it is an easy matter to give the probability distribution for X as requested here. Find all the outcomes where X=2, (where the numbers add up to 2), and add up their probabilities.  Do likewise for X=3, X=4, and X=5.  For example, "12" and "21" are the outcomes in your original sample space where X=3, since 1+2=3 and 2+1=3, so you would add those two probabilities together to get P(X=3).

Conditional Probability!  Again, I would use the original sample space the help solve this problem, following the steps I outline in my book to solve conditional probability.

Similar to my Lesson 6, #18.  Make a three-circle Venn Diagram, and then the answers to all of the questions are pretty straightforward.  Again, be mindful that some of these questions are conditional probability.

I teach you how to interpret P-values in Lesson 2, #6.  Be careful though, those were interpretations for P-values for the mean.  Now you are interpreting for the mean difference in matched pairs, so be careful in your wording.

I would make two-way tables here, then use my check mark method as outlined in the Venn Diagram section to help solve this.  Be careful, because you are sampling without replacement.  Note that you don't have to list all four suits (making a four by four table for example to represent the first two selections).  They are only interested in S, spades.  You could just use two outcomes, Spades, and Spades-complement for each selection, so that means you only have 8 outcomes after three cards have been selected.

You prove independence (or lack of same) by using the independence multiplication rule.  Read page 315 in my book for similar examples of computing P(A and B) and P(A or B) directly from the sample space (the never-fail way to compute any probability).  You can compute P(A and H) directly from the sample space, too.  Then, if A and H are independent, the P(A and H) will equal P(A) times P(H).

Similar to my Lesson 6, #1(d) and (e).  Also, more examples in Lesson 7, #1-3.

You have two normal distributions, M (math score) and V (verbal score).  You want M > V.  The key is to pull everything to one side as M - V > 0.  That's the key, we really want to find the probability that the difference in the scores (M-V) is greater than 0.  You can use the properties of sum and difference for mean and variance I teach at the start of Lesson 4 to work out the mean and variance of M-V.  You also know that M-V is normal.  Let X=M-V, find the mean and variance of X, and find P(X>0).

Of course, to change your score into a z-score, you will have to use the standardizing formula you first learned in Stat 1000, z = (x - mu)/sigma or z = (x - μ)/σ.

Step 1: Find the P(X>85) for the given normal distribution using z = (x - μ)/σ.

Step 2: You have now computed the percentage of the population that scores above 85 on the test.  That percentage you have just computed in step 1 is the p for a binomial distribution where n=10. Find the probability that at least one scores above 85.  I teach the binomial distribution and solving problems involving it in Lesson 7, #4-9.

Step 1: Find the area of the given circle and multiply by 0.2 to get the average number of trees in that circular area.

Step 2: Solve the probability they want.  I teach the Poisson Distribution in Lesson 7, #13-17.

This is chi-square two-way table stuff as I teach in Lesson 9, #1-4.  Be sure to read the section in my book entitled Is it a test for homogeneity or a test for independence? starting on page 537.  Then you can best determine how to state the hypotheses for this test as they request in question 16.  Then this just takes you through all the steps to conduct the hypothesis test like my questions in Lesson 9.

This is clearly a chi-square goodness of fit question as I teach in Lesson 9, #5-11.  It is especially similar to my #8 and #9(a).