Statistics How To

Probability of an Event, Given Another Event

Probability and Statistics > Probability > Probability of an event, given another

Probability of an Event, Given Another Event: Overview

If you’re faced with a question about the probability of an event, given another event, what these problems are really asking you is “given a certain situation, what is the probability that something else will happen?” For example:

  • If I drive, what are my chances of having an accident?
  • If I fly, what are my chances of a flight delay?

These are called dependent events. If you are unsure whether or not you have a dependent event, see: Dependent or independent? This how-to will guide you through the short set of steps to finding the probability for dependent events.

Probability of an Event, Given Another Event: Steps

probability of an event

Surveys often involve dependent events.


Sample question: Find the probability that the answer was no, given that the respondent was male.
Survey Results

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


  • Step 1: Find the number for both the events in the question happening together. In our sample, question, we were asked for the probability of no + male. From the table, the number of males 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!

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If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Probability of an Event, Given Another Event was last modified: October 12th, 2017 by Stephanie

3 thoughts on “Probability of an Event, Given Another Event

  1. James

    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.