Spell checking software catches nonword errors

Event A Occurs

1. Event A occurs with probability 0.2. Event B occurs with probability 0.9. Events A and B

A. are disjoint.
B. are reciprocating.
C. cannot be disjoint.
D. cannot be independent.
2. Choose an American adult at random. The probability that you choose a woman is 0.54. The probability that the person you choose has never married is 0.24. The probability that you choose a woman who has never married is 0.11. The probability that the person you choose is either a woman or never married (or both) is therefore about

A. 0.67.
B. 0.78.
C. 0.13.
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the random number Y can take any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height 0 elsewhere.

3. Is the random variable Y discrete or continuous? Why?

A. Continuous, because the length of the interval is finite.
B. Discrete, because we do not know the number that will be chosen.
C. Discrete, because the sample space {0, 2} is finite.
D. Continuous, because there is an infinite number of values in the interval.

4. What is the height of the density curve between 0 and 2? Draw a graph of the density curve.

5. Use your graph of the density curve and the fact that probability is area under the curve to find P(Y ≤ 1).
Spell-checking software catches "nonword errors" that result in a string of letters that is not a word, as when "the" is typed as "teh."
When undergraduates are asked to type a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution:

6. Is the random variable X discrete or continuous? Why?

A. Continuous, because there can be all sort of errors.
B. Continuous, because all the probabilities are between 0 and 1.
C. Discrete, because we do not know the number of errors in advance.
D. Discrete, because it has a finite number of possible values: 0, 1, 2, 3, 4.

7. What is the probability of the event "at least one nonword error"?
8. Which one of the following statements describes the event X ≤ 2 ?

A. More than 2 nonword errors.
B. At least 2 nonword errors.
C. Less than 2 nonword errors.
D. No more than 2 nonword errors.

9. What is the probability of the event X ≤ 2 ?
10. Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then

A. P(A and B) = 0.64.
B. P(A or B) = 0.70.
C. P(A or B) = 0.64.
D. P(A and B) = 0.70.