Question

MAT 203E: Assignment 2.2

Need detail answers please ——— answer the following:

1. Why is probability useful for making better decisions? Your answer should include some discussion of the nature of probability, how we arrive at different probability outcomes, where we might get pertinent data, and how risk seeking or risk averse we are vis-à-vis probability percentages.
   
2. Select variables that a Las Vegas casino might use in picking the probability of the Super Bowl winner six months before the game is played.
   
3. Select what conditions could change over the course of the regular season that would require the same casino to revise its probability of the Super Bowl winner, or at least the odds of it winning the Super Bowl.

Answer 1

Probability alone is not sufficient to make better decisions. A probabilistic approach should always be supported with some kind of statistical inferences in order for it to give some definite results. This helps to avoid risk and take informative decisions.

The first important thing that we need to realise that many decisions that we make involve uncertainty and probability is a mathematical tool that helps us to quantify and ascertain these uncertainties, provided that the problems are rational and quantifiable. For example, you cannot use probability to find out your suitable match.

For any situation that you are trying to analyse, you create what is known as Sample Space, these is a set of possible outcomes of the situation you are dealing with. Within each sample space, there might be some specific outcomes that you are looking at, these are known as Events.

There are five things you need to know about probability:

1. The list of possible outcomes must be complete.
2. The list of possible outcomes must not overlap.
3. If an outcome is certain to occur, it has probability 1.
4. If an outcome is certain not to occur, it has probability 0.
5. If we add together the probabilities for all the possible outcomes, the total must equal 1.

Every business also deploys probability while making important decisions about the business, for better investments, for better customer service outcomes, competitive strategy and product design. Now, some major concepts in probability are:

• Mutual Exclusivity/Independent Events - Two events are said to be mutually exclusive if the occurrence of one event does not have any effect on the occurrence of the other one. For example, two different people who want to go and see a movie, their decisions pertaining to the type and the timings will be mutually exclusive.
• Dependent Events - Two events are said to be dependent when the occurrence of one event depends on the occurrence of the other one. Going back to the previous example, if there are 2 friends, then their decisions of the type and timings will depend on the likes, dislikes and spare time of each other.

How do we arrive at the possible outcomes of any event is solved using the Counting Principle. It states that the number of choices or outcomes for two independent events, A and B taken together, is the product of the total number of outcomes for each event. So, for a given event, you can divide it into subevents, which should be independent. Then, calculate their individual outcomes and multiply them to get the total number of outcomes. For example, if a person has 2 choices for choosing a dress, she may look at the colors - Red, Blue, Pink and the type - Lace,Flowy.

For the first choice there are 3 different outcomes.

For the second choice there are 2 different outcomes.

The total number of outcomes is 3×2=6.

Risk aversion is a measure of how much people want to avoid risk. Suppose we present an individual with the following gamble:

• With 99 percent probability, you lose nothing.
• With 1 percent probability, you lose $1,000.

The expected value of this gamble is −$10. Now ask the individual how much she would pay to avoid this gamble. Someone who is risk-neutral would be willing to pay only $10. Someone who is risk-averse would be willing to pay more than $10. The more risk-averse an individual, the more the person would be willing to pay.

The fact that risk-averse people will pay to shed risk is the basis of insurance. If people have different attitudes toward risky gambles, then the less risk-averse individual can provide insurance to the more risk-averse individual. There are gains from trade. Insurance is also based on diversification, which is the idea that people can share their risks so it is much less likely that any individual will face a large loss.

Moving on to the Las Vegas example, there can be various categorical and numerical variables that can be taken into consideration while determining the winner of the Super Bowl six months prior. Some of them can be:

• Previous Winners
• No of times each has won the title
• Whom they played against
• Time
• Team Composition
• Best player
• Bet Amount on the teams

Now, time of the match and team composition might change thus leading to a change in the initial predictions of the casino. These are just some of the examples of the variables. There can be many more. Thank you.