There was a typo in my tips for question 6 below that caused some confusion.

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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 and Lesson 7: Discrete Probability Distributions in my book (if you have it) to prepare for this assignment.  

To type in formulas you are using and to show your numbers subbed into the formulas you can click the Equation Editor button in the toolbar that looks like the Sigma Summation symbol (you have to click the "..." other options button to see the sigma formula input button.  Then click the various buttons to make your fractions and enter the symbols.  However, the Equation Editor is extremely slow and clunky.  Personally, I would never use it.  Just type ordinary text explaining what you are doing if you think you should show some work.

I show you how to determine a Sample Space through the use of two-way tables if necessary in Lesson 6 of my book.  Note that all you are asked for is the sample space in each part, so your answer would be something like this (don't forget to use those squiggly brackets "{}").For example, here is the sample space for the outcome of flipping a coin twice where H=heads and T=tails: 

{HH, HT, TH, HH}.

Don't state the probabilities!  You are not asked for the probabilities.  In fact, in many of the situations students will be given for this problem, it is impossible to know the probabilities.  You are just asked for the sample space.

You may find a tree diagram helpful for part (c).  Note that the outcomes will vary in length.  If you get G right away, you stop, but if you get S or C, you select again.  Remember, this is without replacement, so there will be a limited number of trials until the gold coin is selected.  Sample space would look something like this: {G, SG, CG, ...}

Part (d) is similar to part (c) but will be longer.

Although this question appears to be a 3-circle Venn diagram problem (similar to my Lesson 6, question 18), they have left key information out that renders it not worth the effort to try to make the diagram right away.  You are better off just taking each question as it comes and answering it directly.

You can use a Two-way table to list all the outcomes in your sample space first, but, be careful!  You are sampling without replacement.  That will affect the probabilities.  The probability of the second coin depends on what was chosen first.  For example, P(GG) = 7/25 * 6/24 = 0.07.  Work out the complete probability distribution perhaps to assist you in answering all the questions.
Note, the expected value is the mean value.  I show you how to compute mean and variance of X in Lesson 6, question 1 and I also do it more thoroughly in Lesson 7, questions 1 to 3.

You have two normal distributions, J (javelin distance) and H (hammer distance).  You can use the properties of mean and variance I teach at the start of Lesson 4 to work out the mean and variance of J + H.  Since J and H are both normal distributions, J + H is also normal.  You can also compute the mean and variance for J - H.  You also know that J - H is normal.

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.

Part (a)

We want J < H.  Rewrite that as J - H <  0.  So, let X = J - H using the mean and variance for J = H using properties of mean and variance, and find when X<0 on the X bell curve.

Let X = J + H and find the appropriate area on the X bell curve using the mean and variance for J + H.

We want J = H.  Rewrite that as X = J - H = 0.  Think carefully! What are you shading on your bell curve?

I cover the Binomial Distribution in Lesson 7.  If you are ever asked to decide if a particular situation is binomial or not, remember, to be binomial, four conditions must be satisfied:

1. There must be a fixed number of trials, n.
2. Each trial can have only two possible outcomes, success or failure, and the probability of success on each trial must have a constant value, p.
3. Each trial must be independent.
4. X, the number of successes, is a discrete random variable where X = 0, 1, 2, ... n.

I introduce the formula for mean and standard deviation of a binomial distribution in my Lesson 7, question 10.  Be careful that you are using the correct n and p for each question since they keep switching which flight and how many years and flights they are talking about.  Note that n is the total number of flights he has taken to a specific destination during the time period, not just the number that arrive on time.  I think they want you to understand that he is making 6 trips each year, and on each trip he has to take 3 flights.  So there are 6 first flights, 6 second flights and 6 third flights each year.

Therefore, if the question is talking about Flight 1 for one year, then n=6.  Similarly, for Flight 2 or Flight 3.  However, if the question is talking about 2 years, then n is doubled; 3 years would triple n.

Standard Poisson stuff as taught in Lesson 7.  Make sure you are using the correct value for lambda.

Part (c) is really saying that there are 0 trees within a 1.5 metre radius.  What would be the average number of trees in that radius?  They don't tell you how many decimal places to use, so I would compute the average to 4 decimal places, our default number of decimals.

Standard Poisson stuff as taught in Lesson 7.  Make sure you are using the correct value for lambda.