Which of the following are the events in which the probability of occurrence of any one event is not affected by the occurrence of any other events?
Statistically Independent EventsDefinition(s): Show
Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A
and B) = P(A)P(B)). Glossary CommentsComments about specific definitions should be sent to the authors of the linked Source publication. For NIST publications, an email is usually found within the document. Comments about the glossary's presentation and functionality should be sent to . See NISTIR 7298 Rev. 3 for additional details. Contents: Watch the video for how to tell the difference between dependent and independent events:
Dependent vs Independent events Can’t see the video? Click here. What is a Dependent Event?When two events are dependent events, one event influences the probability of another event. A dependent event is an event that relies on another event to happen first. Dependent events in probability are no different from dependent events in real life: If you want to attend a concert, it might depend on whether you get overtime at work; if you want to visit family out of the country next month, it depends on whether or not you can get a passport in time. More formally, we say that when two events are dependent, the occurrence of one event influences the probability of another event. Simple examples of dependent events:
What is an Independent Event?An independent event is an event that has no connection to another event’s chances of happening (or not happening). In other words, the event has no effect on the probability of another event occurring. Independent events in probability are no different from independent events in real life. Where you work has no effect on what color car you drive. Buying a lottery ticket has no effect on having a child with blue eyes. When two events are independent, one event does not influence the probability of another event. Simple examples of independent events:
Card exampleThe probability of picking this particular jack is 1/3. Cards
are often used in probability as a tool to explain how one seemingly independent event can influence another. For example, if you choose a card from a deck of 52 cards, your probability of getting a Jack is 4 out of 52. Mathematically, you can write it like this: If you replace the jack and choose again (assuming the cards are shuffled), the events are independent. Your probability remains the same (1/13). Choosing a card over and over again would be an independent event, because each time you choose a card (a “trial” in probability) it’s a separate, non-connected event. But what if the card was kept out of the pack the next time you choose? Let’s say you pulled the three of hearts, but you’re still searching for that jack. The second time you pull out a card, the deck is now 51 cards,
so: How to tell if an event is Dependent or IndependentBeing able to tell the difference between a dependent and independent event is vitally important in solving probability questions. Why? Imagine a single event: winning the lotto. That depends upon you buying a ticket. So winning the lotto and buying a ticket are dependent events. Your odds of winning the lotto if you buy a ticket might be 1/1 million. But what about something unrelated, like driving to work and winning the lotto? Your odds of winning the lotto if you drive your car (and don’t buy a ticket) are zero. So the odds change a lot with different event types. How Can I Figure out what is a Dependent or Independent event?Figuring out whether events are dependent or independent events can be challenging. Not all situations are as simple as they first appear. For example, you might think that your vote for president increases their chances of winning, but if you consider the Electoral College, that isn’t always the case. Your odds of winning $1 Million Monopoly isn’t what you think.You might think you have a chance of winning the top prize in a scratch off game. But the top prize might have already been won when you buy your ticket. For example, at the time of writing, if you purchased ten, two hundred “$1 Million Monopoly” scratch off tickets in Florida, your chances of winning are exactly the same: Zero!. That’s because 0 out of 15 top prizes are remaining! States like Florida keep a “Remaining Prizes” list…but who really checks it?. Dependent or Independent? StepsStep 1: Ask yourself, is it possible for the events to happen in any order? If no (the steps must be performed in a certain order), go to Step 3a. If yes (the steps can be performed in any order), go to Step 2. If you are unsure, go to Step 2. Some examples of events that can clearly be performed in any order are:
Some events that must be performed in a certain order are:
Step 2: Ask yourself, does one event in any way affect the outcome (or the odds) of the other event? If yes, go to step 3a, if no, go to Step 3b. Some examples of events that affect the odds or probability of the next event include:
Some examples of events that do not affect the odds or probability of the next event occurring are:
Step 3a: You’re done--the event is dependent. Step 3b:You’re done--the event is independent. That’s how to find out if an event is Dependent or Independent! Dependent or Independent Event Formulas in ProbabilityThere are more formal ways to
quantify dependent or independent events. You’ll come across these formulas in basic probability. You can use the following equation to figure out probability for independent events: Example: Solution: one person
being a football fan doesn’t have an effect on whether the second randomly selected person is. Therefore, the events are independent and the probability can be found by multiplying the probabilities together: Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together. ReferencesGonick, L. (1993). The Cartoon Guide to Statistics.
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Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free! Comments? Need to post a correction? Please Contact Us. Which of the following events whose occurrence of one event affects the occurrence of the other?Dependent events in probability means events whose occurrence of one affect the probability of occurrence of the other.
What is the probability of occurrence of an event?The probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring. In the very simplest cases, the probability of a particular event A occurring from an experiment is obtained from the number of ways that A can occur divided by the total number of possible outcomes.
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