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Chapter 6: Q. 3 (page 353)

Spell-checking Spell-checking software catches "nonword errors," which result in a string of letters that is not a word, as when "the" is typed as "teh." When undergraduates are asked to write a 250-word essay (without spell-checking), the number Xof nonword errors has the following distribution:

(a) Write the event "at least one nonword error" in terms of X. What is the probability of this event?

(b) Describe the eventX≤2in words. What is its probability? What is the probability thatX<2.

Short Answer

Expert verified
  1. The probability is 0.9
  2. The probabilities are0.6and0.3.

Step by step solution

01

Part(a) Step 1: Given Information 

Given in the question that,

We have to find the probability of the event.

02

Part (a) Step 2: Explanation 

Consider the random variable Xwhich represents the number of nonword errors.

X≥1could be written as the least non-word error.

The probability is calculated as follows:

P(X≥1)=1-P(X<1)

=1-P(X=0)

=1-0.1

=0.9

03

Part(b) Step 1: Given Information 

Given in the question that,

We have to find what is the probabilityX<2

04

Part (b) Step 2: Explanation 

X≤2indicates that there are two or less non-word mistakes.

The probabilities could be estimated in the following way:

P(X≤2)=P(X=0)+P(X=1)+P(X=2)

=0.1+0.2+0.3

=0.6

Now,

P(X<2)=P(X=0)+P(X=1)=0.1+0.2=0.3

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