You are involved in making one of three possible decisions in your company. There are four states of nature that are being considered. The payoffs and losses appear in the following matrix. Decisions State Nature 1 State Nature 2 State Nature 3 State Nature 4 Maximin Decisions Payoffs? Decision 1 40 -20 10 -2 Decision 2 -10 30 -5 20 Decision 3 0 60 10 -40 Assume you estimate the probabilities of the states of nature to be as follows: P(N1) = .6 P(N2) = .2 P(N3) = .1 P(N4) = .1 Under these conditions which decision would you choose: D1, D2, or D3? Now assume that probabilities on the states of nature cannot be estimated. This makes the issue one of “decision making under uncertainty.” If you want to use the Maximin Strategy (maximizing your minimum gain) which decision would you make? You may use the last column in the payoff matrix to write in your Maximin payoffs. Is there anything else in this payoff matrix that might not have been considered?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
- You are involved in making one of three possible decisions in your company. There are four states of nature that are being considered. The payoffs and losses appear in the following matrix.
|
Decisions |
State Nature 1 |
State Nature 2 |
State Nature 3 |
State Nature 4 |
Maximin Decisions Payoffs? |
|
Decision 1 |
40 |
-20 |
10 |
-2 |
|
|
Decision 2 |
-10 |
30 |
-5 |
20 |
|
|
Decision 3 |
0 |
60 |
10 |
-40 |
|
- Assume you estimate the probabilities of the states of nature to be as follows:
P(N1) = .6 P(N2) = .2 P(N3) = .1 P(N4) = .1
Under these conditions which decision would you choose: D1, D2, or D3?
- Now assume that probabilities on the states of nature cannot be estimated. This makes the issue one of “decision making under uncertainty.” If you want to use the Maximin Strategy (maximizing your minimum gain) which decision would you make? You may use the last column in the payoff matrix to write in your Maximin payoffs.
- Is there anything else in this payoff matrix that might not have been considered?
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