Math 1 Quiz: Two Way Tables
5 questions · exam conditions
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Two Way TablesQuestion 1 of 5

A survey of 500 customers examined their shopping method (online vs. in-store) and purchase amount (under $100 vs. $100+). The results showed that 180 customers made purchases under $100, 70 customers shopped online and spent under $100, and 290 customers shopped in-store. How many customers shopped online and spent $100 or more?

140 customers
150 customers
160 customers
170 customers
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Math 1 Quiz

Math 1 Quiz: Two Way Tables

Practice Two Way Tables in Math 1 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Two Way Tables, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A survey of 500 customers examined their shopping method (online vs. in-store) and purchase amount (under $100 vs. $100+). The results showed that 180 customers made purchases under $100, 70 customers shopped online and spent under $100, and 290 customers shopped in-store. How many customers shopped online and spent $100 or more?

  1. 140 customers (correct answer)
  2. 150 customers
  3. 160 customers
  4. 170 customers
Explanation: Total customers = 500. In-store shoppers = 290, so online shoppers = 500 - 290 = 210. Customers under $100 = 180, online shoppers under $100 = 70. Online shoppers $100+ = 210 - 70 = 140. Other choices represent common arithmetic errors.

Question 2

A survey of 120 students asked about their preferred study location (Library or Home) and their class year (Freshman or Sophomore). The results showed that 45 freshmen preferred the library, 25 freshmen preferred home, 30 sophomores preferred the library, and 20 sophomores preferred home. If a student is randomly selected from those who prefer studying at home, what is the probability that the student is a freshman?

  1. 59\frac{5}{9} (correct answer)
  2. 514\frac{5}{14}
  3. 25120\frac{25}{120}
  4. 724\frac{7}{24}
Explanation: First, identify the marginal frequency for students who prefer home: 25 freshmen + 20 sophomores = 45 total students prefer home. Among these 45 students who prefer home, 25 are freshmen. Therefore, P(Freshman|Home) = 2545=59\frac{25}{45} = \frac{5}{9}. Choice B incorrectly uses total sophomores (50) instead of total who prefer home. Choice C gives the joint probability P(Freshman and Home). Choice D uses an incorrect denominator calculation.

Question 3

A researcher collected data on 150 participants' exercise habits (Regular or Occasional) and diet type (Vegetarian or Non-vegetarian). She found that 40% of all participants exercise regularly, 30% are vegetarian, and 60% of vegetarians exercise regularly. How many non-vegetarian participants exercise occasionally?

  1. 87 participants
  2. 72 participants (correct answer)
  3. 63 participants
  4. 78 participants
Explanation: Build the two-way table step by step: Total regular exercisers = 150 × 0.40 = 60. Total vegetarians = 150 × 0.30 = 45. Vegetarians who exercise regularly = 45 × 0.60 = 27. Therefore: vegetarians who exercise occasionally = 45 - 27 = 18, non-vegetarians total = 150 - 45 = 105, non-vegetarians who exercise regularly = 60 - 27 = 33, and non-vegetarians who exercise occasionally = 105 - 33 = 72. Choice A subtracts regular from total incorrectly. Choice C uses 90 - 27 instead of 105 - 33. Choice D adds occasional vegetarians to a wrong base.

Question 4

A company surveyed 200 employees about work location preference (Office or Remote) and department (Sales or Marketing). If 35% work in Sales, 45% prefer remote work, and the probability that a randomly selected employee works in Sales AND prefers remote work is 0.21, what is the marginal frequency for Marketing employees who prefer office work?

  1. 88 employees
  2. 72 employees
  3. 58 employees (correct answer)
  4. 46 employees
Explanation: Set up the two-way table: Sales employees = 200 × 0.35 = 70, Marketing employees = 200 - 70 = 130, total preferring remote = 200 × 0.45 = 90, Sales employees preferring remote = 200 × 0.21 = 42. Therefore: Sales preferring office = 70 - 42 = 28, Marketing preferring remote = 90 - 42 = 48, Marketing preferring office = 130 - 48 = 58. Choice A incorrectly uses 130 - 42. Choice B uses total office workers (110). Choice D uses Sales preferring office plus an error.

Question 5

A school collected data on 180 students' transportation method (Bus or Car) and lunch location (Cafeteria or Outside). The data shows that 23\frac{2}{3} of students eat in the cafeteria, 59\frac{5}{9} take the bus, and 910\frac{9}{10} of bus riders eat in the cafeteria. What fraction of students who eat outside take the car?

  1. 56\frac{5}{6} (correct answer)
  2. 23\frac{2}{3}
  3. 45\frac{4}{5}
  4. 712\frac{7}{12}
Explanation: Build the two-way table: Students eating in cafeteria = 23×180=120\frac{2}{3} \times 180 = 120, eating outside = 60, taking bus = 59×180=100\frac{5}{9} \times 180 = 100, bus riders eating in cafeteria = 910×100=90\frac{9}{10} \times 100 = 90. Therefore: bus riders eating outside = 100 - 90 = 10, car riders eating outside = 60 - 10 = 50, total eating outside = 60. Fraction of outside eaters taking car = 5060=56\frac{50}{60} = \frac{5}{6}. Choice B would result from using 4060\frac{40}{60}. Choice C from using 4860\frac{48}{60}. Choice D from incorrect probability calculation.