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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鈭�M) Interpret this value in context.

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

Short Answer

Expert verified

Part (b) P(B鈭�M)=0.7227

Part (c)P(Bc鈭�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鈭�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鈭�Mc)=1鈭�P(B鈭�M)P(Bc鈭�Mc)=1鈭�0.7227=0.2773

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