Probabilities can be calculated from tables by determining the frequency of a specific event, and the total frequency for all events.

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 |

The probability that a student travels to school by car is the total for the cars column (7) divided by the total for all journeys to school (31). P(car) = `frac(7)(31)`.

The colour of each car entering a car park is noted. What is the probability of a car chosen at random being red?

White | Red | Blue | Green | Black | Silver | TOTAL |

8 | ? | 7 | 5 | 3 | 5 | 38 |

There are 10 red cars. The probability of it being a red car is P(red) = `frac(10)(38)` = `frac(5)(19)`

Answer: `frac(5)(19)`

The type of transport used by students to travel to school is noted below. What is the probability that a student will take a bus or a train 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 |

All students are being considered: total frequency = 31

7 students (2 + 5) travel by bus; and 3 students (1 + 2) travel by train.

P(bus or train) = `frac(10)(31)`

Answer: `frac(10)(31)`

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