Mobile device users were classified by gender (male and female) and by the social media they use most often (Facebook, Twitter, or You Tube). 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 is his or her gender and most used social media. 

Let's analyze the scenario based on the setup provided:

1. **Total Sample Size**: We have a total of 60 mobile device users.
2. **Classification by Gender and Social Media**: Users are categorized by gender (male or female) and the social media platform they use most often (Facebook, Twitter, or YouTube).
3. **Sample Breakdown**: There are 10 males and 10 females sampled for each social media platform. This results in:
   - 10 males who use Facebook
   - 10 males who use Twitter
   - 10 males who use YouTube
   - 10 females who use Facebook
   - 10 females who use Twitter
   - 10 females who use YouTube

Given this setup, we can calculate probabilities and other measures related to this classification. 

### Probability Calculations
If a user is selected at random, here are some probabilities we can compute:

1. **Probability of selecting a male user**:
   \[
   P(\text{Male}) = \frac{\text{Total males}}{\text{Total users}} = \frac{30}{60} = 0.5
   \]

2. **Probability of selecting a female user**:
   \[
   P(\text{Female}) = \frac{\text{Total females}}{\text{Total users}} = \frac{30}{60} = 0.5
   \]

3. **Probability of selecting a user whose most-used social media is Facebook**:
   \[
   P(\text{Facebook}) = \frac{\text{Total Facebook users}}{\text{Total users}} = \frac{20}{60} = \frac{1}{3} \approx 0.333
   \]

4. **Probability of selecting a male who uses Twitter most often**:
   \[
   P(\text{Male and Twitter}) = \frac{\text{Males using Twitter}}{\text{Total users}} = \frac{10}{60} = \frac{1}{6} \approx 0.167
   \]

5. **Probability of selecting a female who uses YouTube most often**:
   \[
   P(\text{Female and YouTube}) = \frac{\text{Females using YouTube}}{\text{Total users}} = \frac{10}{60} = \frac{1}{6} \approx 0.167
   \]

Would you like more details or have any specific questions?

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Here are five related questions to deepen understanding:
1. What is the probability of selecting a user whose most-used social media platform is YouTube?
2. What is the probability of selecting a user who is either male or a Facebook user?
3. What is the probability that a randomly selected user is female and uses Twitter?
4. If we know a user prefers YouTube, what is the probability that they are male?
5. What is the probability of selecting a user who is either a male or a YouTube user?

**Tip**: When calculating probabilities in categorized data like this, break down each category clearly to ensure accurate calculations.

Mobile device users were classified by gender (male and 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 is his or her gender and most used social media.

Explore the probability analysis of mobile device users classified by gender and social media usage. This study involves 60 users (30 males, 30 females) sampled equally across Facebook, Twitter, and YouTube, providing insights into selection probabilities for gender and platform preference.

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