Mutually Exclusive Write For Us
Mutually Exclusive Write For Us- Mutually exclusive events are events that cannot occur simultaneously. In other words, if one event occurs, the other events cannot occur. For example, when you flip a coin, the event “heads” and the event “tails” are mutually exclusive. If you get heads, then you cannot also get tails.
Another example of mutually exclusive events is the event “raining” and the event “not raining.” If it is raining, then it cannot also not be raining.
Mutually exclusive events are important in probability and statistics. For example, if you want to calculate the probability of event A or event B, you need to know whether or not the events are mutually exclusive. If the events are mutually exclusive, you can add the probabilities of the two events together. However, suppose the events are not mutually exclusive. In that case, you need to subtract the probability of both events occurring simultaneously from the sum of the probabilities of the two events.
Examples Of Mutually Exclusive Events
- A coin toss can result in either heads or tails, but not both.
- A person can be either alive or dead, but not both.
- A person can be either male or female, but not both.
- A product can be either in or out of stock, but not both.
- A person can be either employed or unemployed, but not both.
Mutually exclusive events are often contrasted with independent events. Individualistic events do not affect the probability of other events occurring. e.g., the outcome of one coin toss does not influence the outcome of the next coin toss. Therefore, coin tosses are independent events.
Mutually exclusive events, on the other hand, can affect the probability of other events occurring. e.g., the probability of drawing a red card from a deck of cards is lower if you have already drawn one. Therefore, drawing red cards from a deck is not an independent event.
Mutually Exclusive Events Are Also Called Disjoint Events.
Mutually exclusive events are important in many different fields:
- Logic: Mutually exclusive events are used in logic to create logical arguments. For example, you could argue that if a person is alive, they cannot be dead. This argument is valid because “being alive” and “being dead” are mutually exclusive.
- Probability: Mutually exclusive eventsare used in probability to calculate the probability of different outcomes. For example, you could calculate the chance of flipping a coin and getting heads or tails.
- Statistics: Mutually exclusive events are used in statistics to analyze data. For example, you could use mutually exclusive events to create a contingency table to analyze the relationship between two variables.
How To Use Mutually Exclusive Events To Calculate The Probability Of Different Outcomes:
Suppose you have a bag containing ten red marbles and ten blue marbles. You draw one marble from the bag at random. What is the probability of drawing a red marble or a blue marble?
We need to add the probabilities of drawing a red and blue marble to calculate this probability. However, we must be careful not to overcount the probability of drawing a red and blue marble simultaneously. Drawing a red marble and drawing a blue marble are mutually exclusive events.
Therefore, the probability of drawing a red marble or a blue marble is:
- P(red marble or blue marble) = P(red marble) + P(blue marble) – P(red marble and blue marble)
Since the probability of drawing a red marble and a blue marble at the same time is zero, we can simplify the equation to:
- P(red marble or blue marble) = P(red marble) + P(blue marble)
The probability of drawing a red marble is 10/20 = 0.5. The expectation of drawing a blue marble is also 10/20 = 0.5. Therefore, drawing a red or blue marble is expected to be 0.5 + 0.5 = 1.
This example shows how to use mutually exclusive events to calculate the probability of different outcomes.
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