Question

1. there are 25 students in your class, and 4 are on the track team. you want to know the probability that two students, chosen at random, are both on the track team.
2. are the events independent or dependent?
3. calculate the probability of the event described.

Explanation:

Step1: Determine event - type

When the first student is chosen, it affects the probability of choosing the second student. So the events are dependent.

Step2: Calculate the first - student probability

The probability that the first student is on the track team is $\frac{4}{25}$ since there are 4 track - team students out of 25 total students.

Step3: Calculate the second - student probability

After one track - team student is chosen, there are 3 track - team students left out of 24 total students. So the probability that the second student is on the track team given the first one is on the track team is $\frac{3}{24}$.

Step4: Calculate the joint probability

For dependent events, the joint probability is the product of the probabilities of each event. So the probability that both students are on the track team is $\frac{4}{25}\times\frac{3}{24}=\frac{12}{600}=\frac{1}{50}$.

Answer:

1. Dependent
2. $\frac{1}{50}$