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3.5 Venn Diagrams

Drawing a sample space as overlapping regions to see unions, intersections and complements, and turning English wording into set operations.

Introductory Business Statistics 2e, 3.5 Venn Diagrams

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22 exercises

3.5 Exercise 9

A set of 40 people are selected randomly. 24 are male, 16 are female, 21 like coffee, and 19 like tea. Answer the following using Venn diagrams.

  1. Draw a Venn diagram simply showing the sets of male and female.
  2. Draw a second Venn diagram illustrating 14 males liking coffee.
  3. Draw a situation with a region depicting female and not liking tea.
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3.5 Exercise 11

A set of 40 random people is taken. 15 are male, and 25 are female. 18 people like coffee. 10 people are male and like coffee. Find the probability of selecting a person that likes coffee or is male.

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3.5 Exercise 12

Now, we can use this table to answer probability questions. The following examples are designed to help understand the format above while connecting the knowledge to both Venn diagrams and the probability rules.

What is the probability that a selected person both finished college and is a woman?

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3.5 Exercise 13

Now, we can use this table to answer probability questions. The following examples are designed to help understand the format above while connecting the knowledge to both Venn diagrams and the probability rules.

What is the probability of selecting either a woman or someone who finished college?

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3.5 Exercise 14

Now, we can use this table to answer probability questions. The following examples are designed to help understand the format above while connecting the knowledge to both Venn diagrams and the probability rules.

What is the probability of selecting a high school graduate if we only select from the group of men?

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3.5 Exercise 15

Now, we can use this table to answer probability questions. The following examples are designed to help understand the format above while connecting the knowledge to both Venn diagrams and the probability rules.

Can we conclude that the level of education attained by these 200 people is independent of the gender of the person?

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3.5 Exercise 16

The table shows a spread of what 100 random people like to eat. The columns represent the fruit that they like to eat, and the rows separate the individuals by men and women.

Answer the following questions:

  1. What is the probability that a selected person likes pomegranate and is a man?
  2. What is the probability of selecting either a man or someone who likes apple?
  3. What is the probability of selecti…
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3.5 Exercise 18

Find P(musician is a man ∩\cap had private instruction).

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3.5 Exercise 20

Are the events “being a woman musician” and “learning music in school” mutually exclusive events?

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3.5 Exercise 23

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Latino…

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3.5 Exercise 25

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Latino…

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3.5 Exercise 27

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Latino…

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3.5 Exercise 31

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are women is 48.60. Of the women, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of the licensed U.S. men drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

Complete the following.

  1. Construct a table or a tree…
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3.5 Exercise 33

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are women is 48.60. Of the women, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of the licensed U.S. men drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

Approximately 86.5% of Americans commute to work by…

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3.5 Exercise 35

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

What is the probability that a randomly selected senator has an “Other” affiliation?

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3.5 Exercise 37

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

What is the probability that a randomly selected senator is a Democrat and up for reelection in Year B?

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3.5 Exercise 39

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

Suppose that a member of the U.S. Senate is randomly selected. Given that the randomly selected senator is up for reelection in Year B, what is the probability that this senator is…

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3.5 Exercise 41

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

The events “Republican” and “Up for reelection in Year B” are ________

  1. mutually exclusive.
  2. independent.
  3. both mutually exclusive and independent.
  4. neither mutually exclusive nor ind…
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3.5 Exercise 43

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

the table gives the number of participants in the recent National Health Interview Survey who had been treated for cancer in the previous 12 months. The results are sorted by age,…

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3.5 Exercise 45

Find P(hit was made by Ty Cobb | The hit was a Home Run).

  1. 418912351\frac{4189}{12351}
  2.  1171723\frac{ 117}{1723}
  3. 17234189\frac{1723}{4189}
  4. 11712351\frac{117}{12351}
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3.5 Exercise 47

In a previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data were compiled into the following table.

For the following, suppose that you randomly select one player from the 49ers or Cowboys.

  1. Find the probability that his shirt number is from 1 to 33.
  2. Find the probability that he weighs at most 210 p…

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3.5 Exercise 49

Find P(Blue bead).

  1. 15 36 \frac{15}{36}
  2. 10 36 \frac{10}{36}
  3. 10 12 \frac{10}{12}
  4. 6 36 \frac{6}{36}
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Adapted from Introductory Business Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Business Statistics 2e. Imported at revision 50ec917.