Spell-checking software catches \"nonword errors,\" which are strings of letters

Question

Spell-checking software catches "nonword errors," which are strings of letters that are not words, as when "the" is typed as "eth." When undergraduates are asked to write a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution.

Value of X 0 1 2 3 4

Probability 0.10 0.26 0.26 0.20 0.18

(a) Sketch the probability distribution for this random variable.

(b) Write the event "at least one nonword error" in terms of X.

[multiple choices]

1. X 2

2.X > 1

3.X 1

4.X 1

What is the probability of this event?

(c) Describe the event  X 3 in words.

  [multiple choices]

1.no more than four nonword errors

2.less than three nonword errors    

3.more than three nonword errors

4.no more than three nonword errors

What is its probability?

What is the probability that X < 3?

Explanation / Answer

a) P(X = 0) = 0.1

P(X = 1) = 0.26

P(X = 2) = 0.26

P(X = 3) = 0.20

P(X = 4) = 0.18

b) Option-3) X > 1

P(X > 1) = 1 - P(X = 0) = 1 - 0.1 = 0.9

c) Option-1) no more than four nonword errors

P(X < 3) = 1 - P(X = 4) = 1 - 0.18 = 0.82

d) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1 + 0.26 + 0.26 = 0.62

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