How to Tell if an Event is Dependent or Independent

Probability 10 Comments

Being able to tell the difference between a dependent and independent event is vitally important in solving probability questions. This how to tells you how to tell the difference between the two types of events.

Step 1: Ask yourself, is it possible for the events to occur 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:

  • Tossing a coin, then rolling a die
  • Purchasing a car, then purchasing a coat
  • Drawing cards from a deck

Some events that must be performed in a certain order are:

  • Parking and getting a parking ticket (you can’t get a parking ticket without parking)
  • Surveying a group of people, and finding out how many women are against gun rights (because you are splitting the survey into subgroups, and you can’t split a survey into subgroups without first performing the survey!).

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:

  • Choosing a card, not replacing it, then choosing another (because the odds of choosing the first card are 1/52, but if you do not replace it, your are changing the odds to 1/51 for the next draw)
  • Choosing anything and not replacing it, then choosing another (i.e. choosing bingo balls, raffle tickets)

Some examples of events that do not affect the odds or probability of the next event occurring are:

  • Choosing a card and replacing it, then choosing another card (because the odds of choosing the first card are 1/52, and the odds of choosing the second card are 1/52)
  • Choosing anything, as long as you put the items back

Step 3a: You’re done–the event is dependent.

Step 3b:You’re done–the event is independent.

Related posts:

  1. How to find the Probability of an Event, Given Another Event
  2. How to Figure Out Mutually Exclusive Events
  3. How to find the probability of a simple event happening
  4. How to find the probability of an event NOT happening
  5. How to figure out the probability of picking from a deck of cards in probability and statistics
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10 Responses to “How to Tell if an Event is Dependent or Independent”

  1. Hilary Dickert said:

    Sep 20, 09 at 6:46 pm

    This really helped me to determine the difference between dependent and independent events. Based upon your blog, it just occurred to me that our Florida Lottery System is also a dependent event. Dependent upon the number of tickets sold, the sequence of numbers generated by the player or computer, etc… Interesting stuff!

  2. Kalynn Grabau said:

    Sep 21, 09 at 8:36 am

    Awesome, I needed a better understanding of being able to identify the difference, and this really helped!

  3. Angie Widdows said:

    Sep 22, 09 at 6:30 pm

    this example helped alot. it helped because it asked questions to help you figure out the answer on your own. It allows you to think of ways to interpret whether something is dependent or independent.

  4. Catherine Flanagan said:

    Sep 23, 09 at 5:18 pm

    This blog was very helpful. I like your real life examples and how you put your examples in simple terms.

  5. Lisa Barcomb said:

    Oct 18, 09 at 10:11 am

    At first I wasn’t getting the gest of this dependent and independent statis but now that I read this article on how to do the problems, now I get the whole thing. It seems easy now but before wow some of this can become a nightmare.

  6. How to Do Everything Statistics » How to find the Probability of an Event, Given Another Event said:

    Dec 15, 09 at 10:08 am

    [...] are called dependent events. If you are unsure whether or not you have a dependent event, see How to tell if an event is dependent or independent. This how-to will guide you through the short set of steps to finding the [...]

  7. bonnie said:

    Oct 27, 10 at 6:27 pm

    This really helps me a lot! I’m so confused when I’m doing the review for tmr’s test but now I seem to understand everything! This article makes my life much easier! Thank u a lot ;)

  8. isha said:

    Jan 12, 11 at 8:30 am

    I think their is a typo in the step 1. If the answer to that question is ‘no’ then they are independent events, hence step 3b.

  9. Nabeeha said:

    Aug 31, 11 at 9:34 pm

    Thankyou so much! so if an event occurs in a particular order, it is dependent?

  10. Stephanie said:

    Sep 27, 11 at 4:53 pm

    Hi, Nabeeha,
    Can you post your question on the discussion board? Unfortunately, I don’t have the time to answer math questions here.
    Thanks,
    Stephanie

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