Question

a random sample of students 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.
• 55 people prefer card games rather than board games.

Explanation:

Step1: Fill in the given values

We are given that 50 people who prefer board games also prefer two - player games. So we put 50 in the "Board Games - 2 Players" cell. We are also given that 55 people prefer card games rather than board games. So we put 55 in the "Card Games - 3 or More Players" cell.

Step2: Use the row and column totals

We know that 68 people prefer two - player games. Since 50 people who prefer board games prefer two - player games, the number of people who prefer card games and two - player games is \(68 - 50=18\). So we put 18 in the "Card Games - 2 Players" cell.
We know that 122 people responded to the survey. The number of people who prefer board games is \(50 + 81\) (let the number of people who prefer board games and 3 or more players be \(x\)). The number of people who prefer card games is \(18+55\). And \(50 + 81+18 + 55=122\). Also, since 50 of the people who said they prefer board games prefer two - player games, and the total number of people who prefer board games is \(50 + 81\) (by the fact that the total number of people in the survey is 122 and we already know the number of card - game preferrers). So we can confirm the values.

Answer:

	2 Players	3 or More Players
Card Games	18	55