Conditional Probability Summary

Here’s a reminder of the key points you should know about conditional probability.

The probability of one event, on the condition that another event has occurred, is called a conditional probability.

And we can find conditional probabilities for single actions or multiple actions.

This notation represents the probability of A on the condition that B has happened.

And we can calculate conditional probabilities with this formula.

Where this represents the probability of A and B.

And we call this the intersection of A and B.

In contrast, this represents the probability of A or B.

And we call this the union of A and B.

To calculate conditional probabilities from Venn diagrams, [P(>65 yrs | wealthy)]

start by shading in the area that represents the event we know has happened. [shade area for “Wealthy”]

Then, treat the outcomes in this shaded area as our new sample space. [highlight/pulse outcomes in shaded area]

And, finally, work out the probability as normal by counting the total number of outcomes,

and the relevant outcomes. [highlight the 6 in the overlap area and write 6 at the top of the fraction]

On a probability tree, probabilities after the first set of branches are all conditional on the previous branches having occurred. 

And to calculate the probability of an outcome [P(W  B], multiply the relevant probabilities together,

…which is just our conditional probability formula rearranged. 

Finally, for independent events, the conditional probability is the same as the probability of the event on its own.