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Calculating Probability Using a Venn Diagram

  • 1.

    Below is a Venn diagram that represents the result of a survey of 100 students at a local university on whether they like to play cricket and/or football.

    What is the probability that a student selected at random likes to play cricket only?

    Answers:

    • {eq}\dfrac{7}{20} {/eq}

    • {eq}\dfrac{1}{10} {/eq}

    • {eq}\dfrac{3}{20} {/eq}

    • {eq}\dfrac{9}{20} {/eq}

  • 2.

    70 people of a town were surveyed regarding their interest in reading novels and storybooks. The result of the survey are shown below:

    Find the probability that a person selected at random is not interested in reading novels or storybooks.

    Answers:

    • {eq}\dfrac{1}{2} {/eq}

    • {eq}\dfrac{4}{7} {/eq}

    • {eq}\dfrac{5}{14} {/eq}

    • {eq}\dfrac{3}{14} {/eq}

  • 3.

    Below is a Venn diagram that shows the number of people who like to drink cold drinks and/or lemon juice.

    What is the probability that a person selected at random will not like either choice of drink?

    Answers:

    • {eq}\dfrac{8}{15} {/eq}

    • {eq}\dfrac{2}{5} {/eq}

    • {eq}\dfrac{1}{3} {/eq}

    • {eq}\dfrac{2}{15} {/eq}

  • 4.

    The set of the first positive 20 integers are classified as prime numbers and/or even numbers, and the number of these integers that fall into each category is displayed in the given Venn diagram.

    What is the probability that a number selected at random from the first positive 20 integers is a prime number?

    Answers:

    • {eq}\dfrac{2}{5} {/eq}

    • {eq}\dfrac{1}{10} {/eq}

    • {eq}\dfrac{6}{20} {/eq}

    • {eq}\dfrac{3}{20} {/eq}

  • 5.

    In a company, there are 50 workers. Below is the Venn diagram that shows the number of workers that own Swift cars and/or Sedans.

    Find the probability that a worker selected at random has both a Swift car and a Sedan.

    Answers:

    • {eq}\dfrac{1}{10} {/eq}

    • {eq}\dfrac{1}{5} {/eq}

    • {eq}\dfrac{2}{5} {/eq}

    • {eq}\dfrac{3}{10} {/eq}

  • 6.

    In a class of 60 students, some students like to eat pizza, some like to eat Maggi, some like to eat both, and some do not like to eat either.

    If a student is selected at random, what is the probability that he/she likes to eat only pizza?

    Answers:

    • {eq}\dfrac{7}{60} {/eq}

    • {eq}\dfrac{1}{2} {/eq}

    • {eq}\dfrac{1}{15} {/eq}

    • {eq}\dfrac{1}{20} {/eq}

  • 7.

    A survey was conducted at a university regarding the interests of teachers in reading thriller and mystery novels. Below is the Venn diagram that displays the result of the survey.

    What is the probability a teacher selected at random likes to read mysteries?

    Answers:

    • {eq}\dfrac{62}{115} {/eq}

    • {eq}\dfrac{40}{115} {/eq}

    • {eq}\dfrac{50}{115} {/eq}

    • {eq}\dfrac{12}{115} {/eq}

  • 8.

    The Venn diagram gives the number of ways to roll a multiple of 2 and/or a multiple of 3 when rolling a fair 6-sided die.

    Using the Venn diagram, find the probability of obtaining a multiple of 3 when a die is rolled once.

    Answers:

    • {eq}\dfrac{5}{6} {/eq}

    • {eq}\dfrac{1}{2} {/eq}

    • {eq}\dfrac{1}{3} {/eq}

    • {eq}\dfrac{1}{6} {/eq}

  • 9.

    A survey was conducted by a student in his neighborhood about whether families have cable television or have high-speed internet. Below is the Venn diagram that shows the data collected.

    What is the probability that a family selected at random has both cable and high-speed internet?

    Answers:

    • {eq}\dfrac{56}{145} {/eq}

    • {eq}\dfrac{7}{49} {/eq}

    • {eq}\dfrac{44}{145} {/eq}

    • {eq}\dfrac{2}{29} {/eq}

  • 10.

    58 people are asked if they like a sandwich and/or coffee for breakfast. The Venn diagram shows the results.

    What is the probability that a person doesn't like either one for breakfast?

    Answers:

    • {eq}\dfrac{5}{29} {/eq}

    • {eq}\dfrac{4}{29} {/eq}

    • {eq}\dfrac{15}{58} {/eq}

    • {eq}\dfrac{25}{58} {/eq}

  • 11.

    A teacher of a class organizes a quiz competition of science and mathematics for the students of his class. There are 40 students total in the class. The given Venn diagram represents the number of students who take part in each subject of the quiz competition:

    Find the probability that a student selected at random participates in both science and mathematics.

    Answers:

    • {eq}\dfrac{1}{2} {/eq}

    • {eq}\dfrac{3}{40} {/eq}

    • {eq}\dfrac{7}{20} {/eq}

    • {eq}\dfrac{37}{40} {/eq}

  • 12.

    In a class of 60 students, some students enroll in chemistry, some students enroll in physics, some enrolled in both, and some didn't enroll in either one.

    What is the probability that a student selected at random enrolled in chemistry or physics?

    Answers:

    • {eq}\dfrac{2}{5} {/eq}

    • {eq}\dfrac{5}{12} {/eq}

    • {eq}\dfrac{9}{10} {/eq}

    • {eq}\dfrac{1}{12} {/eq}

  • 13.

    In a town of 100 people, some people speak Tamil, some speak English, some people speak both languages, and some speak neither of the two languages. The number of individuals in each of these categories is displayed in the Venn diagram.

    What is the probability that if any person from the 100 people is selected at random, they will speak both languages?

    Answers:

    • {eq}\dfrac{7}{20} {/eq}

    • {eq}\dfrac{7}{100} {/eq}

    • {eq}\dfrac{12}{25} {/eq}

    • {eq}\dfrac{1}{10} {/eq}

  • 14.

    A group of 55 people was surveyed and asked if they had cats and/or dogs at their homes. The results of the survey are displayed in the given Venn diagram.

    If a person is selected at random from this group, what is the probability that he/she doesn't own either pet?

    Answers:

    • {eq}\dfrac{6}{55} {/eq}

    • {eq}\dfrac{18}{55} {/eq}

    • {eq}\dfrac{28}{55} {/eq}

    • {eq}\dfrac{3}{55} {/eq}

  • 15.

    A toy shop keeps the track of the purchases of customers on a Monday. The shopkeeper classifies purchases as girl's toys and boy's toys, and organizes the number of purchases in the following Venn diagram.

    What is the probability that a customer selected at random purchases a girl toy?

    Answers:

    • {eq}\dfrac{4}{69} {/eq}

    • {eq}\dfrac{8}{69} {/eq}

    • {eq}\dfrac{10}{23} {/eq}

    • {eq}\dfrac{34}{69} {/eq}

  • 16.

    Below is a Venn diagram displaying the preferences of apples and bananas of 50 individuals. What is the probability of an individual in this group preferring apples?

    Answers:

    • 3/10

    • 1/10

    • 2/5

    • 4/5

  • 17.

    The following Venn diagram displays the data of 60 students who use different modes of study (online and offline). Calculate the probability of a student in this group using only offline modes to study.

    Answers:

    • 17/60

    • 19/60

    • 11/20

    • 31/60

  • 18.

    Determine the probability of a student liking Mathematics using the following Venn diagram that shows the results of surveying 30 students on whether or not they like science and/or mathematics.

    Answers:

    • 2/5

    • 13/30

    • 1/30

    • 2/15

  • 19.

    The Venn diagram shown displays the results of a survey done at a coffeehouse of whether customers like tea and/or coffee. Use the Venn diagram to calculate the probability of a customer liking tea.

    Answers:

    • 1/5

    • 2/5

    • 15/35

    • 17/35

  • 20.

    Below is a Venn diagram of the preferences of colors within a group individuals. What is the probability of that an individual in this group prefers the color white?

    Answers:

    • 3/5

    • 12/17

    • 9/17

    • 9/20

  • 21.

    The following Venn diagram illustrates the results of a survey of 35 children about whether they like outdoor and/or indoor games. Find the probability that a child in this group likes to play both types of games.

    Answers:

    • 1/7

    • 8/35

    • 6/35

    • 16/35

  • 22.

    The Venn diagram displays the number of individuals who ate pizza and/or cake at a birthday party with 50 attendees. Identify the probability that an individual at this party ate only pizza.

    Answers:

    • 11/25

    • 11/50

    • 13/50

    • 13/25

  • 23.

    The Venn diagram below illustrates information about 50 children and games they like to play (football and/or basketball). Which of the following choices represents the probability of a child in this group not liking any of the games?

    Answers:

    • 1/2

    • 1/25

    • 3/10

    • 4/25

  • 24.

    Below is a Venn diagram displaying the preferences of 100 employees between taking the bus and/or a car to go to work. What is the probability of an employee in this group preferring both?

    Answers:

    • 9/20

    • 1/100

    • 51/100

    • 3/100

  • 25.

    The following Venn diagram represents the data of 25 individuals about the desserts they like. Calculate the probability of an individual in this group liking only ice cream.

    Answers:

    • 9/25

    • 14/25

    • 6/25

    • 11/25

  • 26.

    Determine the probability of a female liking both home-cooked and canned food using the Venn diagram below, where the Venn diagram displays the results of females surveyed on which of these types of food they like.

    Answers:

    • 5/6

    • 1/6

    • 13/60

    • 2/10

  • 27.

    The Venn diagram below shows the number of individuals in a group of 100 individuals that like Chess and/or Carom. Which of the given choices represents the probability that an individual in this group likes chess only?

    Answers:

    • 7/10

    • 1/10

    • 31/50

    • 1/5

  • 28.

    Below, a Venn diagram displays the preferences of bread or biscuits for 50 people. What is the probability of a person in this group preferring neither bread nor biscuits?

    Answers:

    • 3/50

    • 7/50

    • 16/25

    • 11/25

  • 29.

    The following Venn diagram shows the number of students in a group of 20 students who read comic books and/or history books. Find the probability that a student in this group reads comic books.

    Answers:

    • 1/4

    • 1/10

    • 11/20

    • 3/10

  • 30.

    A group of people were surveyed on whether they like the colors red and/or black. Identify the probability of an individual in this group only liking the red color using the Venn diagram below.

    Answers:

    • 19/50

    • 17/25

    • 2/25

    • 3/10

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