Question

In: Statistics and Probability

According to the Consumer Electronics Manufacturers Association, 10% of all U.S households have a fax machine...

According to the Consumer Electronics Manufacturers Association, 10% of all U.S households have a fax machine and 52% have a personal computer. Suppose 91% of all U.S households having a fax machine also have a personal computer. a. What is the probability that a randomly selected US household has a fax machine and a personal computer? b. What is the probability that a randomly selected US household has a fax machine or personal computer? c. What is the probability that a randomly selected US household has a fax machine and does not have a personal computer? d. Are the events fax machine and personal computer independent? Why?

Expert Solution

Let A = Event that household have fax machine

B = Event that household have personal computer

We have,

P(A) = 0.10 P(B) = 0.52 P(B/A) = 0.91

(a) Consider,

By conditional probability

Hence, P( A and B) = 0.091

(b) Consider,

P(A or B) =

By Addition theorem

Hence, P(A or B) = 0.529

(c) Consider,

Hence, P(A and not B) = 0.009

orchestra answered 1 year ago

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