Conditional Probability is the probability of something happening this is dependent on the outcome of a previous event.
For example, a class determines how the students travel to school:
If only part of the set of all events are considered, then the probability for an individual outcome will change.
For example: P(Boy walks or cycles) is `frac(7)(30)`. But if a Boy is picked at random, the probability that he will walk or ride a bike to school is Boy: P(walk or cycle) = `frac(7)(15)`: the denominator has changed because only boys are being considered.
1. A software company is analysing applications by where they are run. The table shows the primary reason for running software on each machine type.
Given a desktop, what is the probability that it will be used for Social applications?
Answer: Given Desktop, P(social) = `frac(5)(49)`
Because Desktops have been preselected, the denominator is the sum of only the desktop events.
2. From the table above, what is the probability that a social app will be running on a tablet?
Answer: Given Social, P(tablet) = `frac(5)(26)`
Social apps have been preselected, so the denominator will be based on the total of the social apps.