Question

A national survey found that 56% of adults ages 25-29 had only a cell phone and no landline. Suppose that three 25-29-year-olds are randomly selected. Complete parts a through c below.

a) What is the probability that all of these adults have only a cell phone and no landline? (Round to four decimal places as needed.)

b) What is the probability that none of these adults have only a cell phone and no landline? (Round to four decimal places as needed.)

c) What is the probability that at least one of these adults has only a cell phone and no landline? (Round to four decimal places as needed.)

Answer #1

The number of adults aged 25-29 out of three who only had a cell phone and no landlines is modelled here as:

a) The probability that all of these adults have only a cell
phone and no landline is computed here as:

= 0.56*0.56*0.56

= 0.175616

**Therefore 0.1756 is the required probability
here.**

b) The probability that none of these adults have
only a cell phone and no landline is computed here as:

= (1 - 0.56)^{3}

= 0.0852

**Therefore 0.0852 is the required probability
here.**

c) Now the probability that at least one of these adults has only a cell phone and no landline is computed here as:

= 1 - Probability that none of these adults have only a cell phone and no landline

= 1 - 0.0852

= 0.9148

**Therefore 0.9148 is the required probability
here.**

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