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Dependent or Independent Event? How to Tell the Difference

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Dependent or Independent?

Dependent or Independent Event

Winning the lottery depends upon you buying a ticket.


Being 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.

Dependent or Independent? Steps

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

That’s how to find out if an event is Dependent or Independent!

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10 thoughts on “Dependent or Independent Event? How to Tell the Difference

  1. Hilary Dickert

    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

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

  3. Angie Widdows

    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

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

  5. Lisa Barcomb

    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. bonnie

    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 ;)

  7. Stephanie

    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

  8. Leelar

    It is such a great way for teaching. it really helps me to understand ….Thank you so much to the person who gives this ideas