# Worksheet: Two-Way Frequency Tables

In this worksheet, we will practice constructing and using two-way tables.

**Q1: **

Which of the following is **not** true about two-way tables?

- AThey are a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.
- BThey describe the relationship between two categorical variables.
- CThey organize data into classes and show the frequency of each class.
- DThey represent a table of counts.

**Q2: **

Daniel wrote 20 letters and had no mistakes. Mason wrote 28 letters and had no mistakes. If a letter is selected at random, what is the probability that the letter has a mistake and was written by Daniel?

- A
- B
- C
- D
- E

**Q3: **

The following table represents the data collected from 200 conference attendees of different nationalities:

Participant | Arabic Speaker | English Speaker | French Speaker | Total Sum |
---|---|---|---|---|

Man | 45 | 40 | 40 | 125 |

Woman | 15 | 20 | 40 | 75 |

Sum | 60 | 60 | 80 | 200 |

Find the probability that a randomly selected participant is an Arabic-speaking woman.

**Q4: **

The following table represents the data collected from 200 conference attendees of different nationalities:

Participant | Arabic Speaker | English Speaker | French Speaker | Total Sum |
---|---|---|---|---|

Man | 45 | 40 | 25 | 110 |

Woman | 20 | 25 | 45 | 90 |

Sum | 65 | 65 | 70 | 200 |

Find the probability that a randomly selected participant speaks both Arabic and English.

**Q5: **

The data about 50 students and the sports they play is shown in the table. What is the probability that a student selected at random is a female who plays basketball?

Tennis | Basketball | Sum | |
---|---|---|---|

Male | 17 | 9 | 26 |

Female | 16 | 8 | 24 |

Sum | 33 | 17 | 50 |

**Q6: **

The table shows the genders and nationalities of 250 people who entered a competition. One person is selected at random to win the prize. What is the probability that the winner is an Italian woman?

Attendence | Italian | Australian | American | Total |
---|---|---|---|---|

Man | 15 | 45 | 85 | 145 |

Woman | 60 | 35 | 10 | 105 |

Total | 75 | 80 | 95 | 250 |

**Q7: **

The data about 50 students and the sports they play is shown in the table. What is the probability that a student selected at random is female?

Football | Basketball | Sum | |
---|---|---|---|

Male | 6 | 5 | 11 |

Female | 17 | 22 | 39 |

Sum | 23 | 27 | 50 |

**Q8: **

The table shows the distribution of 49 students with respect to their gender and whether they regularly exercise or not. If a student is randomly chosen, find the probability that they do ** not ** exercise regularly.

Gender | Exercises Regularly | Does Not Exercise Regularly |
---|---|---|

Male | 11 | 15 |

Female | 16 | 7 |

- A
- B
- C
- D
- E

**Q9: **

225 people have registered for a competition which will randomly select one winner. Their ages and genders are shown in the table. What is the probability that the winner is aged between 18 and 29?

18–29 | 30–39 | 40–49 | 50–59 | |
---|---|---|---|---|

Male | 47 | 12 | 10 | 34 |

Female | 31 | 45 | 33 | 13 |

- A
- B
- C
- D

**Q10: **

Which of the following is **not** a two-way table?

- A
Class A B C Number of Failed Students 10 20 30 - B
Math English Science Girls 50 40 20 Boys 65 30 10 - C
Wearing Yellow Not Wearing Yellow Girls 50 40 Boys 65 30 - D
Like Skateboards Do Not Like Skateboards Like Snowmobiles 50 40 Do Not Like Snowmobiles 65 30 - E
Walk Cycle Male 50 40 Female 65 30

**Q11: **

Elizabeth collected data to see whether there was a relationship between the gender of students and their wearing yellow on the day of the survey. She randomly surveyed her class and the results are as shown.

Gender | Wearing Yellow | Not Wearing Yellow |
---|---|---|

Girls | 10 | 10 |

Boys | 30 | 20 |

What percentage of the girls were wearing yellow? Round your answer to the nearest integer, if needed.

**Q12: **

The two-way frequency table, shown below, displays the data collected from a random group of high-school students regarding whether they like skateboards and/or snowmobiles.

Like Skateboards | Do Not Like Skateboards | |
---|---|---|

Like Snowmobiles | 80 | 25 |

Do Not Like Snowmobiles | 45 | 10 |

How many students participated in the survey?

**Q13: **

A number of students, girls and boys, were asked to choose their favorite subject from math, English, and science. The results are shown in the given two-way relative frequency table.

Math | English | Science | |
---|---|---|---|

Girls | 50 | 40 | 40 |

Boys | 65 | 30 | 70 |

What percentage of the students chose science (approximated to the nearest integer)?