Risk and Uncertainty

Risk and Uncertainty: Please note that this lecture relates to Chapter 10 of the Course Notes (not chapter 9 as stated in the lecture). The example covered is on page 46 of the Course Notes.

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  1. avatar says

    Got the same problem with the expected value but understood the logic now, hope it can help those who are confused:

    The total of all probabilities is 1 so whether you calculate the contract profit separately or together with the other demand profits, it’s all the same.

  2. avatar says

    Sir, for the par b (i) Expected values, why are we taking the profit of the the contract as well and multiplying it by a probability which is for the demand only?

  3. avatar says

    Hello Prof Moffat,

    i have a bit trouble understanding when we were calculating the expected value, for example, contract 300, if we are sure of this 300 units, why we calculated by 2900*0.2, rather 900+2000*0.2, since it’s the 400 units that are uncertain.


    • avatar says

      just saw the below comment, and did a quick cal for

      method in the video : 2900*0.2 +3400*0.3+4400*0.4+5400*0.1 = 4000

      however, 400*5*0.2 + 500*5*0.3+700*5*0.4+900*5*0.1 +300*3 = 3900

      get more confused……

      • avatar says

        Figured out the problem. it was the math in the video that got a problem. should be 3900. Thanks for the nice lecture!

  4. Profile photo of eniola03 says

    Hello John,Thank you very much for your video

    It is really helpful but I want to verify on what you said about the possible profit.,you said we shouldn’t calculate all the profit in the exam as it might take our time in the exam. but what if the marks are allocated according to all the possible profit calculated or It doesn’t matter and Like how many do you think we should calculate in the exam?

    • Profile photo of John Moffat says

      You misunderstood me :-)

      You should calculate all possible profits. What I said was that since the same arithmetic keeps repeating, there is no need to spend time showing the workings for all of them (if you can calculate them straight on your calculator).
      Show workings for a few of them (to prove you know what you are doing) but you don’t need to show the workings for all to them (unless you need workings for your own benefit).

    • Profile photo of John Moffat says

      Who is Mick? There is no Mick working for me on OpenTuition! :-)

      Any scientific calculator will do – the casio FC-200 is fine.

      The only functions that you need for F5 are log, x^n, and n’th root.
      (the same applies for later exams, so you won’t need to by another calculator later :-) If you decide to take P4 then you will need a button with ‘e’ on it, but if it has the above functions then it will certainly have ‘e’ as well!!)

  5. avatar says

    Hello, first of all thank you for the lectures, they are very helpful.
    I only have one question. At b) shouldn’t we add both:
    – the expected profit from the ordinary demand
    – the profit generated by the contract with the special customer
    to get a total resulting profit?
    I.e. for a contract of 800 we get an expected value from ordinary demand as you calculated, of $4,400, and a profit from contract of 800×3 = 2,400, so a total of 6800 (which looks the highest).
    Thank you.

    • Profile photo of John Moffat says


      The profits calculated in (a) for all possibilities already include both the profits from ordinary demand and profits from the contract sales. (And don’t forget anyway that the total production is limited which means that in many of the cases the normal demand cannot be met in full)

    • Profile photo of John Moffat says

      Contribution is the selling price less the variable costs.

      If you are meaning the question in our Course Notes, then the contribution per unit for ‘normal’ sales is $5 (11 – 6), and for ‘contract’ sales is $3 (9 – 6).

      The workings to get the total contribution for each possible outcome are shown in the lecture.

      • avatar says

        Hello John,

        I think what she/he meant is that there was an error in your calculation during the lecture, when the expected value of the contract for 300 was being done.

        Your calculation= $3,400 x 0.3= $ 1120

      • Profile photo of John Moffat says

        Sorry – it was a mistake. (Nobody is perfect :-) Anyway it would only lose me half a mark)

        The answer at the back of the Course Notes is correct, and so I am not going to re-record the lecture.

      • avatar says

        hi john

        The intention wasn’t to show you up , …. This is a paper that I am struggling with and just want to ensure that I maximize the best possible options to help me get through . So please don t get offensive if i question an answer that looks a bit odd :) …. I enjoy your lecture s and just want to ensure after listening to it that I am 100% confident to go on to practice questions….. nb I actually find your presentation style way better than my present lecturer

  6. avatar says

    thanks so much to opentuition for this kindness. my only and most worrying problem has to do with the constant break in connection. i would be more thankful if there should be any way these videos could be downloaded.

  7. avatar says

    Hello, I have one question: when we calculate expected value why do we multiply the whole profit by the probability? I mean, we are only unsure of the demand value, not the contract which is certain.

    • Profile photo of John Moffat says

      You must always calculate the expected proft. I am guessing that you just want to calculate the expected deman (in units) but this will not give you the right answer (except by coincidence). (If you don\t believe me try some extreme values and see what happens – fo example a profit of 100 from the contact units and $1 per unit from normal demand :-) )

      • avatar says

        Thank you for your answer. I just realized that my question was a bit silly as the results will be the same. What I was trying to understand was why we multiply the total profit (both from the contract and normal demand) by the probability, why not multiply profits from normal demand and just add the profit from the contract after that to get the expected value (cause profits from demand is uncertain and profits from contract is certain):
        For the contract size 500:
        So the expected value for the contract size 500 will be 400+750+1400+350+1500(contract profit 500*3) =4400.
        The answer is the same cause the probability for the contract is 1.
        Sorry just needed to get to math and common sense inline)))

      • avatar says

        Is John Moffat is teaching this…I think its not his accent and he teaches extremely brilliantly. Please let me know I am worried.

        Many Thanks

      • avatar says

        I do have had the same problem as ekadoro did. So for the sake of understanding thoroughly: Can you explain why we multiply the total profit (both from the contract and normal demand) by the probability, Mr Moffat?

        I do know that it may easier for you to display the calculations. But that does not show the logic behind of the probability(or still I dont understand the way you think abt probability in this question).

        Thanks in adv.

      • Profile photo of John Moffat says

        Here is a simple example to illustrate the idea of expected values.

        Suppose the profit per day was 100 with probability of 0.1 and 200 with probability of 0.9.
        Effectively it would mean that out of every 10 days, 1 day would give 100 and 9 days would give 200.

        So what is the average profit per day? If you add up the profit over 10 days (1 at 100 and 9 at 200) you get 1900. Divide by 10 and you get an average of 190 per day.

        Easier is just to multiply by the probabilities and add up:
        (100 x 0.1) + (200 + 0.9) = 190.

        In this question we need to know the average total profit, so we calculate all the total profits that can occur and then multiply by probabilities to get the average.

      • avatar says

        “why not multiply profits from normal demand and just add the profit from the contract after that to get the expected value (cause profits from demand is uncertain and profits from contract is certain)”. That’s what I dont understand.

        For the contract size 500:
        So the expected value for the contract size 500 will be 400+750+1400+350+1500(contract profit 500*3) =4400.

        But you did:

        500units = (0.2x 3,500)+(0.3×4,000)+(0.5×5,000)=4,400

        0.2 or 0.3 are probability of the demand not the contract. So why do u multiply the probability with all the profit(in fact they-the probabilities- are just belong to the original demand and the probability for the contract is 1 or certainty). Why do you come to that way of thinking? Or you do that just because you think that makes your calculation easier? I know that is the same result but It makes me confuse the way you calculate.
        Like ekadoro, I just needed to get to math and common sense inline.
        Hope you clarify my confusing,
        Thank you very much, Mr Moffat.

      • Profile photo of John Moffat says


        You could certainly do what you have written and get the same answer if all the was required was the expected value.
        However, part (a) specifically asks for all possible profits that could result (and almost always that is part (a) when it is asked in the exam).
        My table does show all possible total profits, but your workings do not show each possible total profit, and so you would lose marks even though you have got the correct expected values.

      • avatar says

        Dear Mr John,
        I totally agree the way you answer (a) question that means show all possible profits by contracting pay-off table.
        At (b) expected profit question, I just have had one little confusion about the way you calculate.That’s all, everything else I absolutely agree with your approach. And If you dont mind can you show me why you do that?

        Thank you John.

      • Profile photo of John Moffat says

        OK. In part (a) we have a table showing all the possible total profits for each size of contract that we can choose.

        The only reason that the profits differ for one particular contract size is that there are various levels of normal demand that can occur. We know the probability of each of these levels of normal demand, and therefore the probabilities of each of the different total profit are the same as the probabilities of the level of normal demand.

        As you agreed earlier, you could get the expected profit a different way, but why do more work? We have set up the table of total profits in part (a) because it is required, so easiest is simply to work out the expected total profit using these figures.

      • avatar says

        I knew that we should take advantage the result from (a), but I had not had think that the probabilities of normal demand was the probabilities of total profit, so I didnot dare to calculate that way.

        Everything is fine now.
        Thank you for showing me, Mr John.

      • avatar says

        thanks sir for the quick reply…and i have one other confusion..in the part 2 of this lecture ..for maximax and maximin you were taking the profits horizontally but for the regret table you took the profits vertically why is that????

      • Profile photo of John Moffat says

        We are doing two different things.

        With maximax and maximin we are simply finding the maximum or minimum profit that can be made from each of the choices available to us.

        With minimax regret, we are not basing the decision on the profits that we make, but on the potential profit that we will be losing if we have made the wrong decision.
        So….to produce the regret table by calculating for each possible outcome how much potential profit we would have lost by making each of the possible choices (the difference between the profit we could have made if we had made the best decision and the profit we would actually have made). Then we effectively take a maximin type approach but on the regret table.

        It is a hard thing to explain in words, but I do suggest you watch the part of the lecture again where I go through a very tiny example to explain the logic (and then I apply the same logic to the full question).

      • avatar says

        thanks again for reply sir…i got it i watched the lecture and now i m able to solve the questions….thanks very much..you are the best teacher of f5.. thanks again..

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