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:

Walk | Car | Bike | Bus | Train | Total | |
---|---|---|---|---|---|---|

Girls | 5 | 5 | 2 | 2 | 1 | 15 |

Boys | 4 | 2 | 3 | 5 | 2 | 16 |

Total | 9 | 7 | 5 | 7 | 3 | 31 |

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.

Games | Social | Productivity | Other | |
---|---|---|---|---|

Desktop | 23 | 5 | 17 | 4 |

Laptop | 12 | 7 | 18 | 6 |

Tablet | 21 | 5 | 6 | 7 |

Phone | 18 | 9 | 3 | 4 |

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.

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