Because wireless technology has become reliable and prevalent, many people are t

Question

Because wireless technology has become reliable and prevalent, many people are terminating their landline service. According to a survey by the Centers for Disease Control and Prevention concerning the first half of 2012, 40.6% of households have wireless phones only. In addition, 57.2% have a landline with or without a wireless phone. You may assume that 51% of the population during that time frame were women. The same survey showed that 20.2% of the people are male and only have wireless phones while 21.4% of the people are female and only have wireless phones. a) Suppose the person selected is a man. What is the probability that he only has a wireless phone? (Please include 3 decimal places in your answer.) b) Suppose the person selected only has a wireless phone. What is the probability that the person is a woman? (Please include 3 decimal places in your answer.)

Explanation / Answer

Here we are given that 40.6% of the households have wireless phones only. Therefore,

P( Wireless only ) = 0.406

Now 57.2% of the households have a landline with or without a wireless phone which means that:

P( landline only ) + P( landline and wireless ) = 0.572

Next we are given that P(Women ) = 0.51 which means that P( Men ) = 1 - 0.51 = 0.49

P( Male and Wireless only ) = 0.202

P( female and wireless only ) = 0.214

a) Probability that a man selected only has a wireless phone is computed as:

= Probability that a man has wireless phone only / Probability of selecting a man

= 0.202 / 0.49

= 0.412

Therefore 0.412 is the required probability here.

b) Given that a person selected only has a wireless phone, probability that the person is a woman is computed as:

= Probability that the person selected is women and has wireless only / Probability that a person has wireless only

= 0.214 / 0.406

= 0.527

Therefore 0.527 is the required probability here.

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