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Chapter 5: Q 53. (page 311)

Who eats breakfast? Refer to Exercise 49.

(a) Construct a Venn diagram that models the chance process using events B: eats breakfast regularly, and M: is male.

(b) Find P(B∪M) Interpret this value in context.

(c) Find P(Bc∩Mc) Interpret this value in context.

Short Answer

Expert verified

Part (b) P(B∪M)=0.7227

Part (c)P(Bc∩Mc)=0.2773

Part (a) Venn diagram is

Step by step solution

01

Part (a) Step 1. Given Information   

There are two incidents in this scene.

B: Eats breakfast on a regular basis.

M: Is a man

02

Part (a) Step 2. Concept Used 

A Venn diagram is a visual representation of relationships between things or limited groups of objects using circles. Circles that overlap have similar qualities to circles that do not overlap. Venn diagrams are graphic representations of the similarities and differences between two concepts.

03

Part (a)  Step 3. Explanation 

The model is based on a random process in which event B: Eats breakfast on a regular basis and M: is male.

Venn diagram becomes,

04

Part (b) Step 1. Calculation 

Probability=NumberoffavorableoutcomesTotalpossibleoutcomes

The total number of conceivable outcomes is 595

Therefore, P(B∪M)=110+190+130595=0.7227

05

Part (c) Step 1. Calculation   

P(Ac)=1-P(A)

595 different scenarios are possible.

Therefore,

P(Bc∩Mc)=1−P(B∪M)P(Bc∩Mc)=1−0.7227=0.2773

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Most popular questions from this chapter

Foreign-language study Choose a student in grades 9to 12at random and ask if he or she is studying a language other than English. Here is the distribution of results:

(a) What’s the probability that the student is studying a language other than English?

(b) What is the conditional probability that a student is studying Spanish given that he or she is studying some language other than English?

Sampling senators Refer to Exercise 67. Are events D and F independent? Justify your answer.

To simulate whether a shot hits or misses, you would assign random digits as follows:

(a) One digit simulates one shot; 4and 7are a hit; other digits are a miss.

(b) One digit simulates one shot; odd digits are a hit and even digits are a miss.

(c) Two digits simulate one shot; 00to 47are a hit and 48to 99are a miss.

(d) Two digits simulate one shot; 00to 46are a hit and 47to 99are a miss.

(e) Two digits simulate one shot; 00to 45are a hit and 46to 99are a miss.

Ten percent of U.S. households contain 5or more people. You want to simulate choosing a household at random and recording whether or not it contains 5or

more people. Which of these are correct assignments of digits for this simulation? (a) Odd = Yes (5or more people); Even = No (not 5or more people)

(b) 0= Yes; 1,2,3,4,5,6,7,8,9= No

(c) 5= Yes; 0,1,2,3,4,6,7,8,9= No

(d) All three are correct.

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Stoplight On her drive to work every day, Ilana passes through an intersection with a traffic light. The light has a probability of 1/3 of being green when she gets to the intersection. Explain how you would use each chance device to simulate whether the light is red or green on a given day.

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