GCSE(F),

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 (30). P(car) = `frac(7)(30)`.

1. 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 |
---|---|---|---|---|---|

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

Answer: `frac(1)(3)`

There are 10 red cars. There are 30 cars in total. P(red) = `frac(10)(30)` = `frac(1)(3)`

2. 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 |

Answer: `frac(3)(10)`

All students are being considered: total frequency = 30

6 students (2 + 4) travel by bus; and 3 students (1 + 2) travel by train.

P(bus or train) = `frac(9)(30)` = `frac(3)(10)`

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