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The following table is given to you. If a person is selected at random, find the following probabilities :

The person is a PC user , given she is a female.
The person is Female or uses Mac
The person is Male and uses PC
The person is Male given he uses Mac

1 answer

To solve the probability questions you've posed, I'll need a table of data that provides the relevant breakdown of users by gender and types of computers used (PC, Mac, etc.).

Since you haven't provided that table, I can explain how to compute each probability using hypothetical data. If you can share the actual data, we can compute the exact probabilities based on that.

General Steps to Calculate Each Probability:

  1. The person is a PC user given she is a female.

    • This is a conditional probability, \( P(\text{PC | Female}) \).
    • Use the formula: \[ P(\text{PC | Female}) = \frac{P(\text{PC and Female})}{P(\text{Female})} \]
    • Where:
      • \( P(\text{PC and Female}) \) = Number of females using PC / Total number of individuals.
      • \( P(\text{Female}) \) = Total number of females / Total number of individuals.

  2. The person is Female or uses Mac.

    • This is a union probability, \( P(\text{Female} \cup \text{Mac}) \).
    • Use the formula: \[ P(\text{Female} \cup \text{Mac}) = P(\text{Female}) + P(\text{Mac}) - P(\text{Female and Mac}) \]
    • Where:
      • \( P(\text{Female}) \) = Total females / Total individuals.
      • \( P(\text{Mac}) \) = Total Mac users / Total individuals.
      • \( P(\text{Female and Mac}) \) = Number of females using Mac / Total individuals.

  3. The person is Male and uses PC.

    • This is a joint probability, \( P(\text{Male and PC}) \).
    • Use the formula: \[ P(\text{Male and PC}) = \frac{P(\text{Male and PC})}{\text{Total}} \]
    • Where:
      • \( P(\text{Male and PC}) \) = Number of males using PC / Total number of individuals.

  4. The person is Male given he uses Mac.

    • This is another conditional probability, \( P(\text{Male | Mac}) \).
    • Use the formula: \[ P(\text{Male | Mac}) = \frac{P(\text{Male and Mac})}{P(\text{Mac})} \]
    • Where:
      • \( P(\text{Male and Mac}) \) = Number of males using Mac / Total individuals.
      • \( P(\text{Mac}) \) = Total number of Mac users / Total number of individuals.

Example Calculation:

If you provide the actual numbers for PC users, Mac users, and their breakdown by gender, I can give you the precise probabilities based on that data. Please share the table or specific data for further assistance!