The probability that a student has a part-time job given that they have a cell phone can be calculated using the concept of conditional probability.
1. Identify the relevant information from the question:
- 80% of students have cell phones.
- 45% have part-time jobs.
- 30% have both a cell phone and a part-time job.
2. Determine the probability of a student having both a cell phone and a part-time job:
- This is given as 30%.
3. Calculate the probability of a student having a cell phone and a part-time job separately:
- Probability of having a cell phone = 80%
- Probability of having a part-time job = 45%
4. Use the formula for conditional probability:
- Probability (part-time job | cell phone) = Probability (part-time job and cell phone) / Probability (cell phone)
- Substitute the values:
= 30% / 80%
= 0.30 / 0.80
= 0.375
Therefore, the probability that a student has a part-time job, given that they have a cell phone, is 0.375 or 37.5%. This means that if a student is chosen at random and has a cell phone, there is a 37.5% chance that they also have a part-time job based on the provided survey data.
