Mobile access to social media. The Marketing Management Journal (Fall 2014) published the results of a designed study to investigate satisfaction with the use of mobile devices to access social media. Mobile device users were classified by gender (male or female) and by the social media they use most often (Facebook, Twitter, or YouTube). Consider a similar study in which 10 males and 10 females were sampled for each of the three social media—a total of 60 mobile device users. One of these users is randomly selected. Of interest are his or her gender and most used social media.

a. Use a tree diagram to determine the possible outcomes (sample points) for this experiment.

b. Why should the probabilities assigned to each outcome be equal? Give the value of this probability.

c. Find the probability that the selected user is a female who accesses Twitter most often.

d. Find the probability that the selected user accesses YouTube most often.

Tree diagrams are a means of presenting combinations of two or more events. Each branch is named at the conclusion with its outcome, and the probability is printed alongside the line. Two occurrences are independent if the chance of the first event happening does not influence the probability of the second event happening.

The probabilities given to each outcome are equal to 10 males sampled for Facebook, 10 males sampled for Twitter, and 10 males sampled for YouTube. Similarly, 10 females are sampled for Facebook, 10 females for Twitter, and 10 for YouTube.

Hence, 10 individuals are sampled for each combination of gender and media.

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{assignedtoeachoutcome}\mathbf{\right)}\mathbf{=}\frac{\mathbf{10}}{\mathbf{60}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1}}{\mathbf{6}}\end{array}$

Hence, the probability assigned is1/6.

Number of females are sampled for twitter (f) = 10

Number of individuals are sampled for twitter (n) = 20 (10 female + 10 male).

The probability that the selected user is a female who accesses Twitter is:

$\begin{array}{c}\mathbf{P}\mathbf{(}\mathbf{female}\mathbf{}\mathbf{who}\mathbf{}\mathbf{access}\mathbf{}\mathbf{twitter}\mathbf{)}\mathbf{=}\frac{\mathbf{f}}{\mathbf{n}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{10}}{\mathbf{20}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5}\end{array}$

Hence, the probability of the selected user being a female who accesses Twitter is0.5.

The total number of individuals are sampled (N) = 60

Number of individuals sampled for YouTube (n) = 20 (10 female +10 male).

The probability that the selected users access YouTube most often:

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{YouTube}\mathbf{\right)}\mathbf{=}\frac{\mathbf{n}}{\mathbf{N}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{20}}{\mathbf{60}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{3333}\end{array}$

Hence, the probability of selected users accessing YouTube is0.3333.