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.

Q1:

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

Swimming Climbing Rappelling
14 and Under 15 24 8
Over 14 18 32 24

A child is selected at random. Given that they chose rappelling, find the probability that the child is over 14.

  • A24.7%
  • B75%
  • C48%
  • D51%
  • E19.8%

Q2:

In a group of 96 people, 34 out of the 71 women have a smartphone, and 18 men do not have a smartphone. Determine the probability that a randomly picked smartphone owner in this group will be female.

  • A 7 2 5
  • B 3 4 4 1
  • C 7 1 9 6
  • D 2 5 9 6
  • E 3 7 7 1

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 3 8 7 7
  • B 1 5 2 8
  • C 4 1 1
  • D 1 5 7 7

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.

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