What Is Mutually Exclusive Events In Probability?

# What Is Mutually Exclusive Events In Probability?

Two events are mutually exclusive in statistics and probability theory if they cannot occur at the same time. The estimate of the probability of either happening is affected by knowing whether two events are mutually exclusive.

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The likelihood of two events occurring at the same time is 0 if they are mutually exclusive. Because the likelihood of two events occurring at the same time is zero, the probability of combined occurrences is calculated by adding only the individual probabilities of each event.

The combined probability of events is always 0 since events cannot occur at the same moment. There is no likelihood of a different conclusion if non-overlapping occurrences occur. Mutually exclusive events, also known as non-overlapping events, occur when two or more events occur at the same moment.

## Disjoint Event:

Two or more outcomes that cannot occur at the same time are referred to as disjoint events; in this scenario, the occurrence of one event prevents the occurrence of the other.

Accidents that may occur simultaneously, like as watching a football game and eating popcorn, are examples of occurrences that are not mutually exclusive. And independent events are unrelated outcomes in which the occurrence of one has no bearing on the occurrence of the other.

## Examples:

The outcomes of two characters on fair dice, for example, are independent events. The outcomes 1 and 4 of a single roll of a six-sided die, for example, are mutually exclusive (they can’t both happen at the same time), but they’re not exhaustive (other outcomes are possible; 2, 3, 5, 6).

When a coin is tossed or comes up heads or tails, for example, there are only two outcomes (H, T). When a coin is tossed, for example, either heads or tails will appear, but we cannot receive both. When we toss two coins into the air, we can get three different outcomes, such as both coins coming up heads, both coins coming up tails, or both coins coming up heads and tails.

B is a no-heads event, and C is a heads-on-the-second-coin event. All events with two or more heads must be included. This time, we’ll look at events with odd sums and totals greater than nine. At least one of the outcomes has a probability of one. An equal probability event is one in which the likelihood of one outcome is the same as the probability of the other.

When you roll the dice, you have a 1 in 6 chance of rolling a 5 or a 6, and the sum of the two events equals the sum of the two probabilities. This suggests that the chances of both events A (roll 5) and B (roll 6) occurring at the same time are nil.

## Conditional Probability:

The chance of event A is called the conditional probability if another event B occurs. In its most basic form, the probability is the probability of a specific event occurring when expressed numerically, i.e. probability is a quantitative measure of certainty. Gambling management concerns, such as gambling, coin tossing, dice tossing, and card games, gave rise to probability.

Probability is an area of mathematics that deals with the probability of a random event occurring. Take a few minutes to jot down some ideas about how to calculate probability. Depending on the situation, theoretical probabilities can be calculated using a variety of methodologies. A joint probability distribution can be used to determine several things.

## Venn Diagrams:

• Venn diagrams are frequently used to show the probability associated with events. The probability of events A and B are represented by two disjoint sets (i.e., they have no shared elements) in the Venn diagram above. Events E 1, E 2,…, E n are mutually exclusive in probability theory if the occurrence of any of the events E 1 implies the non-occurrence of the remaining n – 1 event.
• Occurrences that are mutually exclusive are frequently confused with events that are independent. Independent Occurrences Independent events are two events in statistics and probability theory where the occurrence of one does not affect the occurrence of the other.
• If the occurrence of one event does not influence the probability of the occurrence of the other, they are said to be independent. If the occurrence of one event in an experiment prevents or prevents the occurrence of all opposing events in the same experiment. Keep in mind that an event is made up of both basic and composite event outcomes. Because there are no other possibilities, these events are meant to be complementary.
• We can’t receive events 2 and 5 at the same time when we roll the dice. There are two methods for determining whether or not a given event pair is mutually exclusive. Mutually exclusive paired phrases always imply that no two statements may be true at the same time.
• Depending on the context, to argue that more than two propositions are mutually incompatible means that one cannot be true unless the other is true, or at least one of them cannot be true. The word or in probability theory denotes the potential that both events will occur.
• The probability formula is defined because the ratio between the number of favourable outcomes and, thus, the total number of outcomes is adequate for realising the possibility.
• We calculate P(C and D) as 2/6 or 1/3 because there are 6 possible numbers for the dice to land on, and two of those numbers (4 and 6) pertain to both event C and event D. We’ll repeat the probability experiment by rolling two dice and summing the numbers that appear.

Also read: Geometry Of Complex Numbers

## FAQs

##### What do you mean by mutually exclusive events?

Mutually exclusive occurrences are those that can't happen at the same time yet aren't deemed independent. Independent occurrences have no bearing on the viability of alternative strategies. Consider the rolling of dice as an example. On a single dice, you can't roll a five and a three at the same time.

##### How do you know if two events are mutually exclusive?

If two events cannot happen at the same moment, they are mutually exclusive. Disjoint is another synonym for mutually exclusive. If two events are discontinuous, the chances of them happening at the same time are nil.

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