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.