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Chapter 3: Q.65 (page 219)

Prove that smoking level/day and ethnicity are dependent events.

Short Answer

Expert verified

Yes, events of probability for smoking level/day and ethnicity are dependent events.

Step by step solution

01

Content Introduction

A contingency table is shown below:

02

Content Explanation

Two events are shown below

E=events for ethnicity

S=event for smoking level per day

To prove two events independent of each other, just prove one from below three conditions:

1.P(E|S)=P(E)2.P(S|E)=P(S)3.P(EAND鈥�S)=P(E)P(S)

it is concluded that P(E)鈮�P(E|S)

Therefore, the events E and S are independent.

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Most popular questions from this chapter

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in

South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 in Oceania (Pacific Ocean

region).

Let A = the event that a country is in Asia.

Let E = the event that a country is in Europe.

Let F = the event that a country is in Africa.

Let N = the event that a country is in North America.

Let O = the event that a country is in Oceania.

Let S = the event that a country is in South America.

Find P(E).

Write the symbols for the probability that a player is an infielder.

U and V are mutually exclusive events. P(U) = 0.26; P(V) = 0.37. Find:

a. P(U AND V)

b. P(U|V)

c. P(U OR V)

A student goes to the library. Let events B = the student checks out a book and D = the student check out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(D|B) = 0.5.

a. Find P(B AND D).

b. Find P(B OR D).

Use the following information to answer the next 12exercises. The graph shown is based on more than 1,70,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

What is the probability that an Emotional Health Index Score is less than 80.2given that it is already less than81.
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