1st Edition

ISBN: 9780618800766

Author: Ron Larson, Lee Stiff, Laurie Boswell, Timothy Kanold

Publisher: Houghton Mifflin-High School

Concept explainers

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

Chapter 6.7, Problem 15E

To determine

To find: the number of e’s and a’s on the page containing 300 letters.

Expert Solution

Answer to Problem 15E

Number of e’s are on the page is 40 and Number of a’s are on the page is 25.

Explanation of Solution

Given information :

The tables give the probability that a letter chosen at random from a page of English text, is given below:

Letter	Probability
e	0.131
t	0.104
a	0.081
s	0.061

Formula used:

The probability of event A is obtained as:

$P(A)=Number of favourable outcomeNumber of possible outcome$

Calculation :

Let $P(e) and P(a)$ be the probability of getting e’s and a’s if a letter is chosen at random.

From the table,

$P(e)=0.131 and P(a)=0.081$

Number of possible outcomes is 300 letters.

Therefore,

$P(e)=Number of e's are on the pageNumber of letters on the page0.131=Number of e's are on the page300Number of e's are on the page=0.131×300Number of e's are on the page=39.3Number of e's are on the page≈40$

And,

$P(a)=Number of a's are on the pageNumber of letters on the page0.081=Number of a's are on the page300Number of a's are on the page=0.081×300Number of a's are on the page=24.3Number of a's are on the page≈25$

Hence,

Number of e’s are on the page is 40 and Number of a’s are on the page is 25.

To determine

To find: the experimental probability that a letter randomly chosen from the sentence is a t and the probability that it is a s .

Expert Solution

Answer to Problem 15E

Explanation of Solution

Given information :

The tables give the probability that a letter chosen at random from a page of English text, is given below:

Letter	Probability
e	0.131
t	0.104
a	0.081
s	0.061

The two sentence contain 60 letters.

Formula used:

The probability of event A is obtained as:

$P(A)=Number of favourable outcomeNumber of possible outcome$

Calculation :

Let $P(t) and P(s)$ be the probability of getting t’s and s’s if a letter is chosen at random.

Number of possible outcomes is 60 letters.

Total number of letter t’s is 5.

$P(t)=Number of t's are on the pageNumber of letters on the pageP(t)=560P(t)=0.083$

Total number of letter s’s is 8.

$P(s)=Number of s's are on the pageNumber of letters on the pageP(s)=860P(s)=0.133$

From the table,

$P(t)=0.104>0.083 and P(s)=0.061<0.133$

Hence,

The experimental probability of choosing t’s is lesser than the probability of choosing t’s

provided in table and experimental probability of choosing s’s is greater than the probability

of choosing t’s provided in table

Chapter 6.7, Problem 14E

Chapter 6.7, Problem 16E

Chapter 6 Solutions

Pre-Algebra

Ch. 6.1 - Prob. 1C Ch. 6.1 - Prob. 2C Ch. 6.1 - Prob. 3C Ch. 6.1 - Prob. 4C Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.2 - 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