## Exam-Style Question on Probability## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 290. This question is similar to one that appeared on a GCSE Higher paper in 2017. The use of a calculator is allowed.

The table shows the shoe sizes of 35 male teachers.

Shoe size | Number of teachers |
---|---|

7 | 4 |

8 | 6 |

9 | 10 |

10 | 12 |

11 | 3 |

Eight of the 35 teachers do not wear socks.

Ralph thinks that if you choose at random one of the 35 teachers, the probability that he either does not wear socks or wears the median shoe size is \( \frac{17}{35} \) because:

$$ \frac{8}{35} + \frac{9}{35} = \frac{17}{35} $$Is Ralph correct? Give a reason for your answer.

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