# Statistics

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*Give all probabilities to two decimal places.

Three daily newspapers are published in a large city. Suppose we have the following facts about the people in the city:

72% read Newspaper A or Newspaper B.
18% read Newspaper A and B.
15% read Newspaper A and C.
12% read Newspaper B and C.
(a) We randomly select one person in the city. The outcome of interest is which (if any) of the newspapers the person reads. How many outcomes are contained in the sample space?

(b) If we randomly select a person in the city, what is the probability that she reads Newspaper A or Newspaper C?

(c) If we randomly select a person in the city, what is the probability that she reads Newspaper B?

(d) Which of the following statements is true?

B and C are independent.

A and B are independent.

A and C are independent.

None of the three pairs of events are independent.

(e) Which of the following statements is true?

A and C are mutually exclusive.

B and C are mutually exclusive.

A and B are mutually exclusive.

None of the three pairs of events are mutually exclusive.

(f) Without doing any calculations, what is the probability that a person reads Newspaper A if we know she reads Newspaper B?

(g) What is the probability that a randomly selected person reads Newspaper C but not Newspaper B?

(h) What is the probability that a randomly selected person reads Newspaper C if we know she does not read Newspaper B?

(i) What is the probability that a randomly selected person reads exactly two of the three newspapers?

(j) What is the probability that a person reads Newspaper A if we know she reads Newspaper C?

(k) If we randomly select seven people in the city, what is the probability that exactly four of them read Newspaper A?

(l) If we randomly select ten people in the city, what is the probability that at least two of them read Newspaper C?

• Statistics -

e)None of the three pairs of events are mutually exclusive