Final answer:
The probabilities for the given scenarios are calculated using frequencies from a contingency table, demonstrating the application of basic and conditional probability.
Step-by-step explanation:
The question relates to the concept of probability. In the scenario provided, students may or may not have their own car and may or may not have part-time jobs. The table shows the frequencies of these categories among the students. Probability is the measure of the likelihood that an event will occur. It is represented numerically between 0 (impossible) and 1 (certain).
Now, let us solve the questions:
- p(a student with a part time job without a car) - To find this probability, we will look at the number of students who do not have a car but have a part-time job (30 students), and divide it by the total number of students (150 students). The probability is 30/150 = 0.20.
- p(no car | does not have a part time job) - This probability is a conditional probability where the event is having no car given that the student does not have a part-time job. To find this, divide the number of students without a car and without a part-time job (24 students) by the total number of students without a part-time job (18+24=42 students). The probability is 24/42 ≈ 0.5714.
- p(part time job | car) - This is another conditional probability where we are looking for the likelihood of having a part-time job given that the student has a car. There are 78 students with a car and part-time job out of 96 students with a car (78+18). So, the probability is 78/96 = 0.8125.
All these examples demonstrate how to calculate probabilities directly and conditionally based on the given information in a contingency table.