Question

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 $X$of 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 event$X\le 2$in words. What is its probability? What is the probability that$X<2.$

Short answer

1. The probability is $0.9$
2. The probabilities are$0.6$and$0.3$.

Step-by-step solution

Part(a) Step 1: Given Information 

Given in the question that,

We have to find the probability of the event.

Part (a) Step 2: Explanation 

Consider the random variable $X$which represents the number of nonword errors.

$X\ge 1$could be written as the least non-word error.

The probability is calculated as follows:

$P(X\ge 1)=1-P(X<1)$

$=1-P(X=0)$

$=1-0.1$

$=0.9$

Part(b) Step 1: Given Information 

Given in the question that,

We have to find what is the probability$X<2$

Part (b) Step 2: Explanation 

$X\le 2$indicates that there are two or less non-word mistakes.

The probabilities could be estimated in the following way:

$P(X\le 2)=P(X=0)+P(X=1)+P(X=2)$

$=0.1+0.2+0.3$

$=0.6$

Now,

$$\begin{gathered} P(X<2)=P(X=0)+P(X=1) \\ =0.1+0.2 \\ =0.3 \end{gathered}$$