How to find the Probability of an Event, Given Another Event

Probability 13 Comments

What these problems are asking you is “given a certain situation, what is the probability that something else will happen?” These 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 answer.

Sample question:

Survey Results

Gender Yes No Total
Male 15 25 40
Female 10 50 60
Total 25 75 100

Sample question “Find the probability that the answer was no, given that the respondent was male.”

  • Step 1: Find the probability of both the events in the question happening together. In our sample, question, we were asked for the probability of no + male. From the table, that is 25.
  • Step 2:>Divide your answer in step 1 by the total figure. In our example, it’s a survey, so we need the total number of respondents (100, from the table).
    25 / 100 = 0.25
  • Step 3:Identify which event happened first (i.e. find the independent variable). In our example, we identified the male subgroup and then we deduced how many answered no, so “total number of males” is the independent event. The question usually gives this information away by telling you “given that the respondents were male…” (as in our question).
  • Step 4: Find the probability of the event in Step 3. In our example, we want the probability of being a male in the survey. There are 40 males in our survey, and 100 people total, so the probability of being a male in the survey is 40 / 100, or .4.
  • Step 5: Divide the figure you found in step 2 by the figure you found in step 4.
    .25 / .4 = 0.625

That’s it!

Related posts:

  1. How to find the probability of an event NOT happening
  2. How to find the probability of a simple event happening
  3. How to Tell if an Event is Dependent or Independent
  4. How to find the probability of selecting a person from a group or committee
  5. Finding the Probability of a Random Event Probability
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13 Responses to “How to find the Probability of an Event, Given Another Event”

  1. Donna Allen said:

    Sep 19, 09 at 9:53 am

    I found this explanation helpful. I find it to be far more helpful for things to explained step by step. I am not finding the book to do this very well. Thankfully this blog is a very good additional resource.

  2. Jennifer Thomas said:

    Sep 20, 09 at 10:45 am

    I’m reviewing the chapters to prepare for the test and find this to be really helpful. I like that it is broken down into steps with a detailed explanation.

  3. Jennifer Thomas said:

    Sep 20, 09 at 10:49 am

    This was very helpful to me. The step by step instructions with detailed explanations are exactly what I needed.

  4. Hilary Dickert said:

    Sep 20, 09 at 7:14 pm

    As far as determining the probability of an event, given another event, once again, I like how you explain these processes in simple steps. Is it always necessary to determine (step #3) which event happened first? It made me also think of “Murphy’s Law”…

  5. Christine Mao said:

    Sep 20, 09 at 8:30 pm

    I found this very helpful as well as what I read in the book. This explantion is clear and the example is very helpful.

  6. Kalynn Grabau said:

    Sep 21, 09 at 8:33 am

    I agree with Donna. I found this step-by-step to be very helpful. I don’t feel the book gives a very good step-by-step process, at least not for me. Thanks for this website!

  7. Karin Martindale said:

    Sep 21, 09 at 11:59 am

    This was one of the most difficult concepts for me to grasp in Chapter 2. I struggled with finding the answer over and over again in Mathzone. It is hard to switch back and forth in MZ between completing the problem and getting help. Laying the solution out step by step the way you explained it really helped. I printed this post out for my notes. Thanks!

  8. Angie Widdows said:

    Sep 22, 09 at 6:24 pm

    theseblogs are very helpful. Our book does not give many, if any, examples of problems. It also does not give definitions of the symbols used. This example is very helpful because it walks thru an actual example of a problem we may encounter

  9. Mary Johnson said:

    Sep 23, 09 at 2:41 pm

    This is definitely more helpful then the book. I got really confused in the guided solution on Math Zone. I’m still a little unsure of which event is dependent?

  10. Vanessa DuBarry said:

    Sep 23, 09 at 5:55 pm

    this blog was very helpful because to me it was way easier to understand it in these simple steps then what is explains in the book. I also learned about the step number three and I it just made it easier to understand it better doing it this way!

  11. Stephanie said:

    Sep 24, 09 at 5:48 am

    Mary, the dependent event is the event that happens because of another event. You having money in your checking account is dependent on you making a deposit, you getting a speeding ticket is dependent on you speeding in the first place, and getting a parking ticket is dependent on parking somewhere you shouldn’t be parking :) I hope that helps a little,
    Stephanie

  12. Lisa Barcomb said:

    Oct 11, 09 at 8:13 pm

    Now this blogI understood and it went step by step and I guess it had the box so that helped me as well. This book that we have isn’t very user friendly, it does not give good examples if any and its real short and not to the point.

  13. James said:

    Feb 25, 11 at 3:54 am

    Wow, this really clarified things in my head. So many od the stats and math sourses are so obscure and arcane it makes access difficult for those of us who are not oriented to that way of thinking. I think this was both an interesting and useful desription. Thank you.

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