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

**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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