A university has 1500 students out of which 500 are history students, 800 are English students and 200 are both history and English students. Are the events of a student being an English student or a history student independent ?
Yes. Just because a student is an English student does not necessarily make them a history student as well. And vice-versa.
☺☺☺☺
To determine if the events of being an English student and being a history student are independent, we can compare the probabilities.
First, let's find the probability of a student being an English student. We divide the number of English students (800) by the total number of students (1500):
P(English student) = 800 / 1500 = 0.53 (approximately)
Next, let's find the probability of a student being a history student. We divide the number of history students (500) by the total number of students (1500):
P(History student) = 500 / 1500 = 0.33 (approximately)
Now, let's find the probability of a student being both an English and history student. We divide the number of students who are both English and history students (200) by the total number of students (1500):
P(English and History student) = 200 / 1500 = 0.13 (approximately)
If the events of being an English student and being a history student are independent, then the probability of both events happening should be equal to the product of their individual probabilities:
P(English student) * P(History student) = 0.53 * 0.33 = 0.1749
However, since P(English and History student) = 0.13 ≠ 0.1749, we can conclude that the events of being an English student and being a history student are dependent.