Mutually Exclusive Assignment Help

Mutually Exclusive Definition

Mutually exclusive is a term of statistics which describes two or more events which cannot happen simultaneously. It is generally used to describe a scenario in which the occurrence of one outcome supersedes the other. Events are generally considered to be mutually exclusive when they cannot happen at the same time. This concept often comes up in the world of business in the assessment of deal making as well as budgeting. When the mutually exclusive options are taken into consideration, the company should weigh the opportunity cost, or what it would be giving up by choosing every option. The time value of money is generally taken into consideration when a decision is made between two mutually exclusive choices. Mutually exclusive events are the events which cannot happen both, but should not be considered as independent events. For instance, while rolling a dice, we cannot roll both a five as well as three simultaneously on a single dice.

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What does Mutually Exclusive Mean?

If two things are mutually exclusive, they are separate as well as very different from one another so that it is impossible for them to happen together. In statistics the events are describes as mutually exclusive when they cannot happen at the same time. The probability for event Y to happen if event X occurs will always be zero. For instance, if a coin is flipped, the two possible results of the action are mutually exclusive because the appearance of one side will instantly eradicate the possibility for the other side to spear. From the standpoint of the business, mutually exclusive scenarios are evaluated in the situations of capital budgeting.

An Example of Mutually Exclusive

Suppose a kid wants to go to school. There are two ways, one that takes him to the school and the other one that can take him home. Which path will be chosen by him? He will definitely choose either one of the paths since he cannot choose both at the same time. This is an example of mutually exclusive where two events cannot occur at the same time.

The mutually exclusive concept is very often applied in capital budgeting. Organisations might have to make a choice between multiple projects which will add value to the organisation upon completion. Some of these projects are mutually exclusive.

An organisation which manufactures wallets for men is presently evaluating all its opportunities of investment for the coming years. The organisation might have three options for investing its resources. The first option is increasing the plant installed capacity, for meeting an increasing demand. The seco

nd project is a training centre for the youth, for teaching them skills for working for the organisation and the third is a project to renew the computer equipments of all the staffs. Since the main priority is the expansion of the plant, it was considered an independent project which will be approved as long as the net present value is more than zero. As for the rest of the two projects, they are mutually exclusive since the resources of the company can only fund one of them.  After the financial calculations were made, the new computers were given approval as they offered a higher net present value which comes from an increase in the overall productivity of the staff.

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Mutually Exclusive Events

Mutually exclusive events are the things which cannot happen at the same time. For instance, a person cannot run backwards as well as forward at the same time. The events running forward as well as running backwards are mutually exclusive events. Similar kind of event is the tossing of a coin. A coin cannot be tossed with getting both heads and tails. So tossing a coin as well as tossing a tail is mutually exclusive.

Mutually exclusive is generally confused with independent events but they two are different concepts. Unlike mutually exclusive events, independent events can happen simultaneously. The independence of events shows that the outcome probability of one event does not influence the outcome probability of the other event. The concept of mutually exclusive provides many applications in finance. An event as such is frequently encountered while the process of decision making in corporate finance. For instance, the process of capital budgeting considers mutually exclusive long term projects of investments. Apart from this, the mutually exclusive events can be identified in investment management. For example, because of some constraints, the managers of portfolio may face limited opportunities of investment. If certain opportunities cannot be4 employed together, they are said to be mutually exclusive. In finance, the event analysis takes into consideration both statistical as well as financial aspects. Apart from the probabilities of the events, the analysis generally involves different financial metrics like the Net present value or some macroeconomics factor.

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How do You Know If The Probability is Mutually Exclusive?

In statistics as well as theory of probability, two events are mutually exclusive if they cannot occur at the same time. The events E1, E2, .......En are said to be mutually exclusive if the occurrence of one of them indicates the non-occurrence of the remaining N -1 events. Thus, two mutually exclusive events cannot both occur.

Despite some of the features of mutually exclusive events, the events still follow certain fundamental probability rules. These rules are as follows:

Rule of multiplication - The rule of multiplication is utilised when there is a need of finding probability of the events occurring simultaneously. The rule of multiplication for mutually exclusive events signifies the following:

P (A intersection B) = 0

Since the events cannot happen simultaneously, their joint probability is always zero.

Rule of Addition - the rule of addition permits the determination of the probability that at least one of the events occurs. For mutually exclusive events, the ruile of addition defines the following:

P (A UNION B) = P (A) + P (B)

The union probability of events is found by adding only the individual probabilities of every event as there is zero probability that both the events occur at the same time.