of 10 The percentage of adult users of the Internet who use Facebook has Interne

Question

of 10 The percentage of adult users of the Internet who use Facebook has Internet users age 50 and older, 54% use Facebook. Assume that 52% of adult Internet users are age 18-49 a. What is the probability that a randomly selected adult user of the Internet is age 50 or older (to 2 decimals)? increased over time Pew Research Internet Pr ect 2013). Of adult Internet users age 18-49 81% u se Facebook or adult Internet user uses Facebook, what is the probability that he/she is age 18-49 (to 4 decimals)? Check My Work (2 remaining) loon Key 657 PM 40 11/1/2017 ^ ype here to

Explanation / Answer

Here we are given that:

P( facebook | 18-49 ) = 0.81 and P( facebook | 50 or older ) = 0.54. Also, we are given that: P( 18 - 49 )= 0.52

a) Now the probability that the adult internet user is 50 or older is computed as:

P( 50 or older ) = 1 - P( 18 - 49 ) =1 - 0.52 = 0.48

Therefore 0.48 is the required probability here.

b) Using law of total probability, we get:

P( facebook ) = P( facebook | 18-49 )P( 18 - 49 ) + P( facebook | 50 or older ) P( 50 or older )

P( facebook ) = 0.81*0.52 + 0.54*0.48 = 0.6804

Now given that an adult internet user uses facebook, probability that he/she is age 18-49 is computed using bayes theorem as:

P( 18- 49 | facebook ) = P( facebook | 18-49 )P( 18 - 49 ) / P( facebook )

P( 18- 49 | facebook ) = 0.81*0.52 / 0.6804 = 0.6190

Therefore 0.6190 is the required probability here.

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