In a group of 40 students, 22 study Economics, 25 study Law, and 3 study neither of these subjects. Determine the probability that a randomly chosen student studies:

1. Both Economics and Law
2. At Least one of these subjects
3. Economics given that he or she studies Law

I really don't understand how to calculuate the 3rd one.

To calculate the probability of an event, we need to divide the number of favorable outcomes by the total number of possible outcomes. Let's break down each question one by one:

1. Probability that a randomly chosen student studies both Economics and Law:

To determine the number of students studying both Economics and Law, we need to find the intersection of the two subjects. We know that 22 students study Economics, 25 study Law, and the total number of students is 40.

Let's define:
E = Students studying Economics
L = Students studying Law
n(E) = Number of students studying Economics
n(L) = Number of students studying Law
n(40) = Total number of students

We can represent the number of students studying both Economics and Law using a formula:
n(E ∩ L) = n(E) + n(L) - n(40)

Therefore, the probability of a student studying both Economics and Law is:
P(E ∩ L) = n(E ∩ L) / n(40)

2. Probability that a randomly chosen student studies at least one of these subjects:

To calculate the probability that a student studies at least one of these subjects, we need to find the union of the two subjects. This includes students studying only Economics, only Law, or both.

The number of students studying at least one of these subjects can be found using the formula:
n(E ∪ L) = n(E) + n(L) - n(E ∩ L)

Therefore, the probability of a student studying at least one of these subjects is:
P(E ∪ L) = n(E ∪ L) / n(40)

3. Probability of studying Economics given that the student studies Law:

To find the probability of studying Economics given the student studies Law, we need to use conditional probability. It is represented as P(E | L).

We know that n(L) = 25. To calculate the number of students studying Economics given that they study Law, we need to find the intersection of Economics and Law, n(E ∩ L).

Therefore, the probability of studying Economics given that the student studies Law is:
P(E | L) = n(E ∩ L) / n(L)

I hope this clarifies how to calculate the third probability. Let me know if you need further assistance!