Question

a random sample of adults are asked about their preferences for games. complete the two - way table so that it has the characteristics listed. • 122 people responded to the survey. • 50 of the people who said they prefer board games said they also prefer two - player games. • 68 people prefer two - player games. • 56 people prefer card games rather than board games. type your answers in the boxes. (table with columns board games, card games and rows 2 players, 3 or more players, with empty boxes for values)

Explanation:

Step1: Find total board games

Total respondents: 122. Card - only: 56. So board games total: \( 122 - 56 = 66 \).

Step2: Find 2 - player card games

Total 2 - player: 68. 2 - player board: 50. So 2 - player card: \( 68 - 50 = 18 \).

Step3: Find 3 + player board games

Board total: 66. 2 - player board: 50. So 3 + player board: \( 66 - 50 = 16 \).

Step4: Find 3 + player card games

Card total: 56. 2 - player card: 18. So 3 + player card: \( 56 - 18 = 38 \). Also, check total 3 + player: \( 16 + 38 = 54 \), and total 2 - player + 3 + player: \( 68 + 54 = 122 \), which matches.

Answer:

2 Players - Board Games: 50
2 Players - Card Games: 18
3 or More Players - Board Games: 16
3 or More Players - Card Games: 38

(In the two - way table, fill the boxes with these values respectively.)