# Worksheet: Conditional Probability: Two-Way Tables

In this worksheet, we will practice dealing with the concept of conditional probability using joint frequencies presented in two-way tables.

**Q3: **

A bag contains 4 red balls and 3 blue balls. I take one at random, note its color, and put it on a shelf. I then take another ball at random, note its color, and put it on the shelf next to the first ball. The figure below shows the probability tree associated with this problem. Are the events of “getting a blue ball on the first draw” and “getting a red ball on the second draw” independent?

- Ano
- Byes

**Q4: **

Daniel and Jennifer are running for the presidency of the Students’ Union at their school. The votes they received from each of 3 classes are shown in the table. What is the probability that a student voted for Jennifer given that they are in the Class B?

Class A | Class B | Class C | Total | |
---|---|---|---|---|

Daniel | 161 | 169 | 177 | 507 |

Jennifer | 147 | 195 | 152 | 494 |

- A
- B
- C
- D

**Q5: **

The two-way table shows the ages and activity choices of a group of children at a summer camp.

Swimming | Climbing | Rappeling | |
---|---|---|---|

14 and Under | 15 | 24 | 8 |

Over 14 | 18 | 32 | 24 |

A child is selected at random. Given that this child is over 14, find the probability, to the nearest percent, that they chose climbing.

- A43%
- B36%
- C57%
- D76%
- E26%

**Q6: **

The table below contains data from a survey of core gamers who were asked whether their preferred gaming platform was the smartphone, the console, or the PC. The gamers are split by gender.

Find the probability that a core gamer chosen at random prefers using a console. Give your answer to three decimal places.

Given that a core gamer prefers to play using a console, find the probability that they are male. Give your answer to three decimal places.

**Q7: **

A fanzine website for the TV show *A Maze in Space* collects data on the number of new alien species
encountered by two starships in each season of the show. The data for seasons 1, 2, and 7 are shown in the
table below, split between the two starships: Zeta and Geoda.

A Maze in Space | ||||
---|---|---|---|---|

New Species Encountered | ||||

Season 1 | Season 2 | Season 7 | Total | |

Starship Zeta | 3 | 3 | 5 | 11 |

Starship Geoda | 28 | 36 | 8 | 72 |

Total | 31 | 39 | 13 | 83 |

Find the probability that a new alien species chosen at random was encountered by starship Geoda. Give your answer to three decimal places.

**Q8: **

A fanzine website for the TV show *A Maze in Space* collects data on the number of new alien
species encountered by two starships in each season of the show. The data for seasons 1, 2,
and 7 are shown in the table below, split between two starships: Zeta and Geoda.

A Maze in Space | ||||
---|---|---|---|---|

New Species Encountered | ||||

Season 1 | Season 2 | Season 7 | Total | |

Starship Zeta | 3 | 3 | 5 | 11 |

Starship Geoda | 28 | 36 | 8 | 72 |

Total | 31 | 39 | 13 | 83 |

Given that a new alien species was encountered in season 7, find the probability that they were encountered by Starship Geoda. Give your answer to three decimal places.

**Q9: **

A fanzine website for the TV show *AMaze in Space* collects data on the number of new alien species encountered by two starships in each season of the show.
The data for seasons 1, 2, and 7 is shown in the table below, split by the two Starships Zeta and Geoda.

AMaze in Space | ||||
---|---|---|---|---|

New Species Encountered | ||||

Season 1 | Season 2 | Season 7 | Total | |

Starship Zeta | 3 | 3 | 5 | 11 |

Starship Geoda | 28 | 36 | 8 | 72 |

Total | 31 | 39 | 13 | 83 |

Given that a new alien species was encountered in season 7, find the probability that they were encountered by Starship Geoda. Give your answer to three decimal places.

**Q10: **

Data is collected from the TV show *AMaze* in Space on the number of new alien species first contact is made with.
The data for Starship Zeta in seasons 1, 2, and 7 are shown in the table below.
The data have also been categorized by whether the crew member who made first contact was male or female.

From the table, find the probability that first contact was made with a new alien species by a female crew member. Give your answer to three decimal places.

Find the probability that first contact was made in season 1 and by a female crew member. Give your answer to three decimal places.

Given that first contact was made with an alien species chosen at random, in season 1, find the probability that first contact was made by a female crew member. Give your answer to three decimal places.

Are the events “S1 = first contact made in season 1” and “female” independent?

- AYes, they are independent.
- BNo, they are not independent.