Conditional Probability Two Way Tables

# Conditional Probability Two Way Tables

GCSE(H),

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:

WalkCarBikeBusTrainTotal
Girls5522115
Boys4235216
Total9757331

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.

## Examples

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.

GamesSocialProductivityOther
Desktop235174
Laptop127186
Tablet21567
Phone18934

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.