Question

A marketing firm would like to test-market the name of a new energy drink targeted at 18- to 29-year-olds via social media. Suppose a study found that 36% of adults (18 and older) do not use social media. Suppose the percentage of adults age 30 and older is 75%. Suppose that the percentage of the adult population that is either age 18–29 or uses social media is 66.7%. (a) What is the probability that a randomly selected adult uses social media?

Answer 1

Answer:

The probability of randomly select an adult that has between 18 and 29 years old and use social media is 22.3%

Step-by-step explanation:

As the test is targeted to 18-to-29-year-old adults using  social media, we want to know the probability that a randomly selected adult uses social media and belong to the study group.

To achieve this, we have this data:

- 36% of all adults do not use social media

- 75% of all adults are >30 years old.

- The percentage of population that is either 18-29 years old or uses social media is 66.7%

Using the last data we have that

$P(social\,media=yes\, or\,18-29=yes)=P(social\,media=yes)+P(18-29=yes)-P(social\,media=yes\, \&\,18-29=yes)\\\\0.667=(1-0.36)+(1-0.75)-P(social\,media=yes\, \&\,18-29=yes)\\\\0.667=0.64+0.25-P(social\,media=yes\, \&\,18-29=yes)\\\\P(social\,media=yes\, \&\,18-29=yes)=0.64+0.25-0.667=0.223$

The probability of randomly select an adult that has between 18 and 29 years old and use social media is 22.3%