Final answer:
The statements B and D from the provided options illustrate conditional probability, which considers the probability of an event based on a condition. To calculate conditional probabilities, such as P(change|bus), you count the students in the condition group and determine how many also meet the criteria of the event of interest.
Step-by-step explanation:
The concept being illustrated in the student's question is conditional probability, which is the probability of an event occurring given that another event has already occurred. To answer the question, let's go through each statement one by one:
- A. Of all students, the probability of choosing a male. This is not a conditional probability because it does not consider another event.
- B. Of the students who walk, the probability of choosing a female. This is a conditional probability because it considers the event that the student walks.
- C. Of all students, the probability of choosing a male who walks. This is not a conditional probability, but rather a joint probability of two events occurring together.
- D. Of the females, the probability of choosing one who rides the bus. This is a conditional probability because it is based on the condition that the student is female.
- E. Of all students, the probability of choosing a student who drives. This is not a conditional probability because no condition is specified.
In conclusion, the statements B and D from the provided options illustrate conditional probability. Statement B considers the condition of students walking and statement D the condition of being a female student.
To calculate an actual conditional probability, you can follow the example provided in the question. If you wish to find P(change|bus), which is the probability that a randomly chosen student has change given that he or she rode a bus within the last month (change AND bus), you count all the students who rode a bus and among them count those who have change. The probability equals the number of students who have change and rode a bus divided by the total number of students who rode a bus.